As this scenario has been bugging me most of yesterday evening at work and this morning, I have done a bit of research and believe the following to be the 'book' answer. I standby for major disagreement.
An air traffic control clearance shall include the following items:
Aircraft identification
Clearance limit
Route
Levels of flight and changes of levels.
A clearance limit is defined as the point to which an aircraft is granted an air traffic control clearance and shall be specified by naming:
(1) an aerodrome
(2) a reporting point, or
(3) a controlled or advisory airspace boundary.
While not mandatory, base leg is a published reporting point in the circuit. Therefore if instructed to 'join base leg' by default this becomes your 'clearance limit'. The AIP then adds, in VMC or IMC, if a pilot is instructed to change frequency to contact another control and fails to make satisfactory two way contact, then the pilot shall revert to the orginal frequency and inform ATC of the situation.
Therefore, by the book, you hold on base leg and go back to approach and tell them you can not get satisfactory two way with the tower.