Thee are projects around the country to support people experiencing feelings of social isolation. Rather than
directly seeking support yourself though, it might be worth considering getting involved to help others (with the benefits then rebounding onto you). In Luton, contact Luton Connecting Communities, on 01992 585961, for further information.
If you're on Facebook, consider making contact with other mothers of young children in your area through the local Mum to Mum group. (You could, for example, make new friends through simply taking your children to the same play centres or activity sessions):
https://www.facebook.com/groups/267675523722134/
If you're able to get a local bus to Luton Airport cheaply, the return fare from there to London Victoria Coach Station is only £11.61 with Megabus when booked in advance. (That might help you save money when visiting your mother). Alternatively a Super Off Peak Day Return rail ticket, valid (among other times) at any time on Sundays, from Luton to St Pancras costs only £11.40. [If you want advice on cheap(ish) travel to a specific area of London, please post again to tell us which part of the capital your mother lives in].