I can sympathize. I dated online for a time, and the stated-height-requirement thing used to drive me either totally, totally nuts or into extended moments of depression, depending on the day. I am not very short, but I am under average, and I was really blown away by the sheer number of women whose stated requirements ruled me out on the basis of height alone. I think the percentage of women who actually write that kind of thing down might really surprise folks who haven't seen it themselves. This stuff can you depressed real fast (the classic lyric "pretty women out walkin' with gorillas down my street" comes to mind), and not just with respect to dating or women. For instance, wall street or other "money" types are very frequently quite tall, and very seldom short. Not saying that there aren't exceptions, but when you are sitting around thinking about your height it sure can be annoying! :)
(Then again, I bet the fact that sooo many men overtly state that they are looking for someone up to but no older than their own age probably amazes/dumbfounds/exasperates the ladies just as much.)
At the time, I eventually realized that the main thing that the women were saying was that they wanted a man taller than their own height--not necessarily taller than other men. (There were a lot of descriptions in their profiles like "must be taller than I am in heels", which always seemed like a clever way to make the "requirement" sound sexy btw.) Anyway, the point is that there are plenty of short girls around, and I went out of dates with a number of very attractive ladies who were shorter than I. Nothing in particular came of it, but I generally had a good time and never felt like I had wasted an evening.
A friend of mine has done lots of research in an academic capacity in this area (using source data from dating sites, speed dating services, etc), and one thing that has been proven rather definitively as far as he is concerned is that ladies behave differently when they are in a "competitive" mating situation such as a speed dating event, bar/club, etc. All the things they say they want in a man (stable, nice, smart, funny) go out the window and they just go for whoever is "hottest". Dating sites appear to trigger many of the same behaviors. But if you look at who they end up with long-term, it's a whole different set of factors that matter (again, not necessarily what they say to themselves or others). I can't provide any source links for this research, and I am massively paraphrasing from memory, but these are, I think, legit gists of some pretty legit findings unless my memory is doing me a terrible disservice today.
As the risk of offending USA-born females who might be reading, I would suggest perhaps trying to focus on ladies from other lands, as from my (all caveats about small sample size noted but notwithstanding) personal experience, the literal-minded "list of requirements" is somewhat of an American-girl-next-door phenomenon. My girl is from one of the lands down under and is the find of the century (and physically well out of what I had perceived to be my league). We are delightfully married in a "soul-mate" style and couldn't be happier. I spend many a moment disbelieving my own luck. FWIW, she is just about the exact same height as I am.
[Edit: I missed that you're from the UK so the USA-biased part of my post here is questionable at best. Sorry!]
I mention my wonderful wife not to brag, hopefully, but just to point out there are so many exceptions to whatever evolutionary/social programming we have (so much noise amongst the signals) that the rules only matter in the aggregate, not to the individual. At least that's my experience, one shortish geek to another. :)
My armchair analysis of my friend's papers, my own experience, and other reading is that both men and women have an elaborate system of truths and deceptions in our heads about what we are looking for in a mate. Many women have this annoying height thing and a bunch of stuff about income (sometimes masked, sometimes not). Many men have similar stuff about age, measurements, etc. Both are, I believe, about trading up genetically--so that our imagined offspring will have a genetic advantage in successive generations. But those are "10,000 foot view" ways of initially identifying potential mates when faced with a big group of them (like "all the guys on this site" or "all the chicks in this city"). On a one-on-one level though, it's a whole different story--a whole different set of things can trigger that "my genese might be able to trade up here" response. And meanwhile, our conscious brains are doing their own thing--getting intrigued, falling in love, etc--which are using a much more sophisticated type of modeling than the crude ">= meanHeight" gating that we think it might be from looking at the "hard" evidence.
Anyway, the main reason I wanted to post a response here was to respond that:
1)Yes, yes, a thousand times yes the "height thing" is a real thing. It feels and appears to be a glass ceiling.
2) It is really frustrating, so frustrating that it's tempting to write the whole enterprise off as the realm of the tanned and shallow.
3) But, as demonstrable as the rules appear to be--the evidence right in front of you--they are illusory and don't actually apply. That's my experience anyway.