You found somewhere to stay then?
For your 5yo, I guess it will be more difficult as most children here are in school now until, at the earliest, the first week of July - most schools break up around mid-July.
Have you tried your local NCT? Phone 0870 444 8707 to find details of your local branch or look on the NCT website . If the branch has a local newsletter, it will may have details of local groups and activities. NCT is mainly based around babies but some branches run 'toddler' groups.
You could take to visiting the museums - we sometimes used to get chatting to people there. In the basement of the Science Museum is an area especially for younger children and there are often mums and children in there. Get in quick though as school trips are thick and fast this half term so the museums get crowded.
The Natural History Museum has a dinosaur area that both children may enjoy. I first too my DD when she was about 2, I think.
My brain seems to be somewhat lacking in function this morning (I blame two nights of less than five hours sleep) but if I think of anything later, I'll post again.
We're in Nottingham which isn't a million miles away but is still around 2 hours by train so not practical to pop round for a coffee
Hope you find some local friends soon.