One place you might try for net access while in London is the Institute for
Historical Research. The IHR is not very far from the PRO and it is open
well into the evening if you don't mind reading/writing e-mail outside of
your own room. There is no cost to use the computer system with access to
internet but there is a cost associated with membership in the Institute.
I'm not sure what the cost of membership is because my department pays for a
couple memberships.
J P Dwyer
University of Colorado