It is possible to not travel as a consultant, but it is difficult. At manager level, you will certainly have to travel to client offices for meetings etc - however if your clients are based in London then that could mean travelling only to within London itself! Quite often consultants do get staffed on long projects in a city or even country other than the one where their home office is, however some firms are more prone to doing that kind of thing than others. Working for a big 4 may involve a bit of travel, but I expect you may be able to avoid travelling abroad for the most part (the odd trip abroad is one thing, but you certainly don't want to get staffed in another country for anything longer than a week or so every now and then).
Also, here's a tip. A lot of people go on about how bad working for the public sector is. However, bear this in mind - you won't be travelling abroad if you work on a public sector assignment! Chances are you may even stay in London, although with public sector there is quite a high chance of having to stay in places like newcastle for an extended period (but at least you're still in the home country, right?). Financial services may be more UK based too, what with London being a financial capital. Energy may well involve international travel - in fact, I'd avoid this. Not sure about telecoms.
Basically I think this is a conversation you need to get out of the way as early as you can. If you haven't signed contracts yet, now is the time to negotiate travel arrangements with them. You may well do well to play the "I have a young family" card as many of the big firms are all into diversity and that kind of thing. You will need to be a little careful how you go about it however (if you have already joined) because some people aren't as friendly and accommodating as others (there is a tendancy to treat people like robots in this industry).
Please do let us know how it all works out and here's keeping our fingers crossed for you.