On being asked this, here's what I came up with.
It occurs to me that half way through the year, everything I'd immediately recommend has already been and gone. What have I missed? Any good upcoming events for a first-timer to not send them running away screaming?
Well, you've missed most of this year's already. :¬) Already been-and-gone for 2013 were Picocon, Eastercon, Redemption, the London Scifi Film Festival & the spring MCM Expo.
For next year, it's a shoo-in. The Worldcon is coming to Europe for its once-a-decade visit. This is the event. First time in England since 1987 (!) although there have been two in Scotland in 1995 and 2005 and one in the Netherlands in 1990. Absolutely essential.
http://www.loncon3.org/ Also next year...
Well, the Scifi Weekender is usually a hoot. Not remotely serious, just a big party. They do have panels but in public open spaces so they're so noisy that you can't hear. OTOH, I've been to all of them and never paid, they give away so many tickets as prizes...
http://www.scifiweekender.com/ The Eastercon is the British national SF con. Strong focus on literary SF with a token presence of comics and media. Streams for those into gaming (not my thing), costuming (really not my thing), filk (SF folk music - run, don't walk away, IMHO). Can be a bit intimidating but I go every year and love it.
Next year it's in Glasgow. Should be a small, friendly, good one.
http://satellite4.org.uk/ The 2nd biggest literary con of the year is my personal fave but it is relatively small and cliquey. Sadly I've missed 3 of the last 10 due to lack of funds. This is the only significant literary con left in 2013. (!)
http://www.novacon.org.uk/index.php Outside the UK, and small but usually a good craic, is the Irish national con, Octocon. It's not on the same scale as UK cons and sadly usually most attendees commute in, rather than staying at the hotel, so it can be a little quieter on the extracurricular activities, but I've enjoyed the 3 or 4 I've been to immensely.
http://www.octocon.com/ Also in Ireland next year is the Eurocon, a follow-on event to the Worldcon in London. This should be great.
http://www.shamrokon.ie/ In other fandoms...
The Discworld Con only happens on even-numbered years. I've missed the last 3 but I hope to be there next year:
http://www.dwcon.org/ Warm, friendly, fun, but Pratchett-only and few of its members go to non-Pratchett events.
Still to come in 2013... Well, there's been one MCM Expo but there will be another in the autumn. They're a big party, rather American-style, with a lot of teens and twenty-somethings. Raucous, colourful, shallow, but a giggle.
http://www.mcmcomiccon.com/london/ Also still to come is at least one London Film & Comic Con, if you are near the capital. Again, somewhat kid-centric, mainly focusses on merchandise & autograph collectors.
http://www.londonfilmandcomiccon.com/ I might just go to these, finances permitting:
Unicon - an occasional series of summertime cons that happen in universities. I've been to about three of them and enjoyed them. They're small, informal, friendly and relaxed.
http://congenial.org.uk/ Nine Worlds Geekfest is a new event that seems to be trying to fuse several different strands of fandom and conventions. Again, if I can afford it, I'll go.
https://nineworlds.co.uk/ Outside of the capital...
Well, there's Collectormania. Only been to a couple. They're pretty much purely commercial - just a chance to buy collectable merchandise and autographs. Not bad but not my thing, personally. The LF&CC is run by these guys.
http://www.collectormania.com/ BTW, on the note of filk, there is an annual (?) filk con. I've never been and I don't expect I ever will, but I thought I probably ought to mention it. NOT a first-time event, though. Go to an Eastercon, see if you like filk - if you are a folk singer, that might help, but then again, my one mate who is a folk-singer went to the filk concert at the last UK worldcon and came away appalled. It's, er, niche. But some of my friends do like it. I just don't understand why.
http://www.contabile.org.uk/semibreve/ Another thing I don't go to are gaming events, as I'm not a gamer. I've been to one or two videogames events, but I don't really do that, either. Some listings here, of which I know nothing:
http://gameconventioncentral.com/uk-england-scotland-wales-britain-ireland/ I know some people who go to Salute, which is a wargaming con, again rather commercially-oriented AFAICT. I've not been myself.
http://www.salute.co.uk/