Yes - I'm aware of at least two:
http://www.puregym.com/gyms/leeds(That one is right by the Corn Exchange. I think membership is about £17 monthly, but with no contract. You can get a day pass for £6.)
http://www.thegymgroup.com/gyms/leeds/(Right on The Headrow. Membership £16 monthly, also no contract.)
Both of these have opened within the past year, and so it seems that the 24/7, low cost, no contract gym concept has started to take off here. Both in city centre. They have promoted themselves as 'no frills' - but Pure Gym does have a few classes, not sure about The Gym. They don't have swimming pools, hot tubs or saunas. It's gym equipment, locker rooms & showers - so basic that way. Also, I do not believe that they have full staff around 24/7 - they are securely locked during off-hours & access is with a key card & there are (I think) CCTV cams & such as part of their security during the wee hours.
A couple of my work friends belonged to Pure Gym at one time & I think they liked it. It started first, then The Gym opened to slightly price undercut Pure Gym, but there's not much in it - meaning £1 cheaper per month is not really a big deal, IMO.
The great thing is you could try it & if you don't like it - well there's no contract.
ETA - Oh yeah, I meant to add, there might be other options out in the 'burbs somewhere, but I'm not aware of any specifically - doesn't mean there aren't any out there.
