Possibility of negotiating a better contract if I am offered an asst prof position? I attended an interview last week for an asst prof position in math in a university in the UK that is much lower ranked than the universities where I did my PhD and postdocs, for instance, my PhD university is one of the top 20 worldwide whereas this university is ranked in the 300-350 bracket. The university is in the city where my girlfriend works hence why I decided to at least apply for the job but I am in no way going to jeopardise my career just to live in the same city as my gf if I decide this is position is not a good move.

Do you think that if I was offered the position I could negotiate a better contract? For example, if I was to request that instead of coming it at the very bottom of asst prof scale, I come in several ranks higher? 

I would be in the running for asst profs jobs in much higher ranked institutions, or I could make alot more money by going to industry which many of former PhD colleagues have done - so from my perpsective if I am to sacrifice positions at better institutions/higher salaries there would have to be some compensation. This is a very big sacrifice since, as far as I understand it, you can step down in the university rankings as much as you want to take a job but you won't be stepping back up..and I imagine it will be much harder to apply for and get funding, etc. coming from a much lower ranked place.

So do you think it is possible to obtain a better contract or is the academic hiring system so rigid in general that there is no room for manoeuvre here and I would be forced to come in at the bottom rung of the ladder?
In the UK, there is typically much less negotiation of entry-level academic contracts, compared to the US market, or general stories of how it was in past. Full professors still can negotiate their contracts, but assuming that it is your first permanent post, I would be surprised if the University would engage in a negotiation with you. Typically, the universities in the UK will match your current academic salary or offer you to start one spine point above it. In exceptional circumstances they can offer two spine points, but "I am making a sacrifice here for you guys" is hardly going to count as a good reason. You are expected to compare your options, and if you indeed have a better deal elsewhere, you'd better take it. Comparing their offer with hypothetical offers you could have got from some industry is likely not going to work.

But before all this becomes a real problem, you need to get their offer first. And to get there you typically would need to pass through the interview and convince the panel that you understand what you are getting into and you are genuinely interested in the opportunity as it is offered to you. If you are less than enthusiastic about this particular university and/or the conditions they offer, I would suggest to try and discuss this during the interview, so that the panel can make an informed decision whether to offer this job to you (and perhaps agree on your conditions) or another candidate. If you confirm your interest in the position during the interview and try to re-negotiate the conditions afterwards, it is quite likely that after some discussion the post will be unfilled and the position has to be re-advertised, which is really quite frustrating to everyone involved.