I came across a similar problem recently.
The answer is to talk to both RTF nicely and agree that one of them will submit the PPL application. This RTF then must, by the time the PPL application is submitted, put the other RTF's instructor on its own list of instructors. Just update the apprpropriate sheet of the form and fax to PLD at the CAA with a covering note for the update.
Voila! Simple, legal, as recommended by the CAA even. Suggest student has custody of own training file and presents it when appearing for lessons at RTF A or RTF B.