The twentieth Leicester Comedy Festival could not have got off to a better, more high profile start if the TV channel that sponsored it was called Richard instead of Dave. By a nice coincidence the remains of the Plantagenet king found in a local car park were confirmed as royal in the run-up to the opening, giving the organisers the chance to make as many "funny bones" puns as they could manage.

I arrived in Leicester on Sunday morning for a whirlwind day of gigs and one of the first things I saw was a ridiculously massive queue of damp people in anoraks. Sadly not waiting for a show but to see Richard's remains. I'm sure, however, that the history buffs descending on Leicester will boost comedy attendances too. The city probably hasn't had so much publicity since Gary Lineker was scoring goals for them.

for my first LCF experience I gave Richard III a body swerve and instead headed to Just The Tonic for Mark Olver's Dancing About Architecture, a comedy geek's dream of a gig previously done in Edinburgh in which he chats about comedy with other comedians. Olver (right) made a fatal, but brilliant error when planning the show. He expected that due to the 1.30pm start there would be some hangover-induced no-shows so he over-invited, only for everyone to turn up. As a result the audience got thoughts and gags from Norman Lovett, Johnny Vegas, Carly Smallman, Adam Hess and Markus Birdman.

Olver was in the fortunate position of not really having to do much. He simply asked the kind of standard questions that would make Jerry Sadowitz combust and the guests did the rest. On being asked whether he ever gets nervous before a gig Vegas revealed that he had been known to "pray for a small fire in the venue" so that a show would be cancelled. "Not for anyone to be hurt," he added.

When it came to talking about their worst gigs, Hess trumped the opposition by recalling a gig where he went on with a damp patch of piss on his crotch and had to leave the stage in shame. Olver pointed out, much to Carly Smallman's surprise, that this can be an occupational hazard and advises anyone with a weak bladder to wear dark clothes. Markus Birdman underlined how addictive stand-up can be by telling the audience that he once did a gig despite having had a stroke earlier in the day. Norman Lovett, meanwhile, called for the return of cut-price third class train travel – "for students, take all the seats out, they'd reallly like it."

The discussion moved on quickly to the state of modern comedy and the divide between mainstream club comedy and comedy as art and self-expression. Interesting things were said about the conservatism of the circuit and how it currently stifles creativity. Then, just as the chat started to feel like a group of workers talking shop Adam Hess revealed that Jimmy Savile once propositioned him. Sort of. He was on a cruise with his dad when Savile walked up to the thirteen-year-old Hess, stuck his finger in some custard and said "do you want some of that?"  Now if that isn't the inspiration for an Edinburgh show I don't know what is.

Annoyingly I had to leave the discussion before the end to join Comedy Tourist, a special event in which the audience was given a guided tour around Leicester and along the way comedians would pop up and do short impromptu sets. As we sat in the wood-panelled Guildhall I realised why Carly Smallman had also left Olver's chat early. She was the first surprise andf warmed the crowd up with a mix of self-deprecating banter about her lack of a love life and  some brisk, twisted songs. Her finale, getting everyone to sing along to Livin' On A Prayer was more Butlins than comedy gold but it got everyone warmed up for their damp walk.

Music turned out to be a theme as the next act Bob Slayer (left), performing in Wygston House, one of the oldest houses in the city, got everyone to clap along to an extraordinary rendition of We Will Rock You. Slayer doesn't really have any jokes, but what he has in abundance is a lot of bottle. By sheer force of personality he got his entire audience to follow him into a freezing cold, timber-framed annexe. And then just left us there...

When we had realised that Slayer was not returning it was on through the positively medieval rain to the Magazine Gateway, a tower next to De Montfort University that used to be a prison. It was starting a feel a little like a hostage situation as we waited to be entertained by the next act, local alumnus Jack Campbell who got some supportive laughs out of explaining how he always thought he had Scottish ancestry until he paid to find his family tree and got a less-than-Braveheart surprise.

The next stop was the courtroom and who should pop up in the judge's chair but none other than Mark Olver. He had clearly come straight from his gig and had no idea what was going on but quickly got up to speed with some puns that would make Tim Vine squirm. But the mix of venue and Olver's natural bonhomie, allowing the audience to play juror and pass a verdict on his act, made it feel like a real event. You may be pleased to hear we let him live to pun another day.

And then it was over to the Newarke House Museum, past the chair that once belonged to Daniel Lambert, the fattest man in Leicester, and into a room where we were greeted by...Bob Slayer, who plucked one of us to play the lead role in his immersive version of The Very Hungry Caterpillar. The rest of the audience breathed easily as the victim spent the rest of the show in a green sleeping bag munching through apples. Despite the foul weather and dodgy jokes Comedy Tourist was a clear success. Better weather and, maybe a running time shorter than two hours, and it should become a regular festival fixture.

There was barely time for a quick break before the next gig, Diane Spencer (right) at The Exchange Bar. This was one of the first performances of Alpha Tattoo that Spencer is going to take to Edinburgh this summer so it would be unfair to give it a full review. But I will say this. I'd seen the famously edgy Sarah Silverman in London the previous night and at times Spencer was much, much filthier. She has a good way with descriptions of genitalia and can certainly spin a yarn, bookending the gig with tales of the fire caused by burning her teenage diary and the time she flew back from Holland next to the pilot. A few less ginger jokes would not go amiss though young lady. We can see the colour of your hair, now move on.

The persistent rain had now turned to snow as I popped into Indian restaurant Kayal for the final gig of the night. The programme was a little behind schedule so I caught the last few minutes of Alan Francis, who I last saw acting his socks off in Cul-De-Sac before Christmas. Francis, bearing a striking resemblance to a young Barry Humphries, was mid-political rant when I walked in, conjuring up a nice image of Cameron and Osborne in a boat sailing away as England sinks. There was so much sleet outside I was starting to worry that Leicester itself might sink so I stayed put and waited for the closing show from Christian Reilly.

In a nice way Reilly's set brought the day full circle and reminded me of the discussion I had watched earlier about the way that club comedy might be crowdpleasing but it rarely breaks down barriers. Reilly is a brilliant musician, who can do spot-on impressions of Springsteen, Elton John and the Arctic Monkeys among others and he got loads of laughs so it would be harsh to knock what he does. But sometimes the jokes are just too cheesy. "I've been a happily married man for two weeks....I've been married for four years." I don't think I've heard that one since the golden age of that old show much admired by Stewart Lee, The Wheeltappers and Shunters Social Club.

OK, stand-up snobbery over, Reilly did make me laugh when he adapted The Pixies Here Comes Your Man and made it about David Cameron leaving his daughter in the pub – There Goes Your Dad. Reilly has worked with Phil Nichol and some of Nichol's manic intensity seemed to have rubbed off on Reilly. He was good at screaming into the mic but not quite as good as Nichol. An entertaining if not revolutionary way to end a whistlestop tour of Dave's Leicester Comedy Festival. Or as they should maybe call it just for this year, Richard III's Leicester Comedy Festival.

Dave's Leicester Comedy Festival runs until February 24. Upcoming highlights include Harry Hill, Alan Davies, Russell Kane and Jenny Eclair. Details here.