I'm currently on ML from a City firm, having got pregnant within two months of qualifying...
In my experience, mature applicants are welcomed. Provided you're willing to start at the bottom and get given the donkey work by associates (since trainees invariably get the rubbish stuff nobody else wants to do) and be patronised on a fairly regular basis (by, for example, the lawyers on the other side, who will throw in as many technical words as possible the moment they realise you're a trainee) then I don't think you're at any disadvantage simply because you're older.
Being pregnant/a mum, however, is a different matter. City trainees have to be in the office whenever your supervisor/partner tells you to be in the office. Some departments have fairly child-friendly hours, but a lot (corporate, banking just to name two) most definitely do not. Partners or senior associates with children are able, to some extent, to tailor their schedules to suit their family life, but as a trainee you are at the bottom of the pile: you are told when you can go home and what time you need to be in the next day. Failure to do this will get you a bad reputation, annoy other trainees/associates who have to pick up your work, and minimise any chance you have of qualifying. The problem is that you will almost definitely have to work in one of these life-sucking departments: my firm insists that every trainee does a seat (a 6m placement) in corporate, for example. Hours are also often irregular (you'll get weeks of working until midnight, and then a week of finishing at 5.30pm), making childcare a nightmare. You'll also have the obligatory 'networking' drinks and events in the evenings. Aligning all this with being pregnant/having a baby is really really hard both physically, practically and emotionally.
In my experience, City firms are against people becoming mums in general (other than when they've already made partner...). It got to the point at my firm that I was embarrassed walking around with a bump: I got so many stares, and so many hurtful comments that I avoided moving around the office as much as possible. Obviously that's just my experience and you may well be very lucky, but I felt so unwelcome there I would never return.
I realise that this is all totally negative and I don't want to put you off if this is truly what you want. If it is, then go for it - you may be pleasantly surprised.
One solution which springs to mind is applying somewhere other than the City. Many regional firms offer TCs and will probably be a lot more amenable to a mum. They'll also have better (by which I mean more regular) hours. Public sector places like the CPS also offer TCs (I think) and they might be worth investigating. The money's nowhere near as good, but it's a trade-off which you might consider worthwhile.
If you're dead-set on the City, though, it might be worth talking to HR of the firms you're interested in (over the phone so they can't see the bump). On a no names basis you could explain your position and ask if there would be any solutions (eg ensuring that you didn't have to work in the transactional departments with the worst hours). Worth a shot.
Sorry I can't be more positive: hopefully someone will come on and tell you it'll all be great. What you want to achieve is probably possible, but it'll be tough.
Sorry also about the length of (and the possible ranting in) this post, but hope it helps in some way..