I've just been checking WAGN trains, this is the message on their website:
THE FOLLOWING SERVICE IS BEING PUT INTO OPERATION. INNER SERVICES HALF HOURLY FROM FINSBURY PARK AT XX.00 AND XX.30 TO WELWYN GARDEN CITY AND AT XX.15 AND XX.45 TO HERTFORD NORTH . SERVICES TO AND FROM PETERBOROUGH AND CAMBRIDGE TERMINATING AT WELWYN GARDEN CITY LEAVING WELWYN GDN CITY AT XX.00 AND 00.30 FOR CAMBRIDGE AND XX.15 AND XX.45 FOR PETERBOROUGH. SERVICES LEAVE PETERBOROUGH AT XX.15 AND XX.45 AND LEAVE CAMBRIDGE AT XX.00 AND XX.30. PASSENGERS FOR MELDRETH, SHEPRETH AND FOXTON JOIN A BUS AT ROYSTON. SERVICES TO KINGS LYNN START FROM CAMBRIDGE. ALL TRAINS STOPPING AT ALL STATIONS.
Obviously, they do also say that this is subject to change and short notice cancellations/alterations etc.
Would guess that other operatorts would be attempting something similar, i.e. running skeleton services as near to London as possible, to stations where they can turn trains round.