Max C,
From experience I must disagree. Unless a specific statement was made by the ATCO, an embedded ATZ clearance is NOT guaranteed or implied by a MATZ clearance.
The only exception I can think of is where the request was made to cross through the airfield overhead or within 2nm / 2.5nm as appropriate) at 2000 feet or less and a positive reply was received, in which case the ATZ clearance would normally be mentioned by ATC in their reply. In that instance ATZ clearance is assured because effectively this is what was requested.
Farnborough DO normally give (us) a clearance and mention either yes or no, avoid, to the Odiham ATZ clearance.
I heard one instance last Sunday where someone was getting a telling off from ATC because he flew through an active ATZ (Benson) whilst under a flight information service from Brize Radar. Brize had obviously followed up his request to penetrate only the Benson MATZ by landline, but he went straight through the ATZ as well.
If you wish to enter an ATZ, you must make your intention perfectly clear to ATC before you do so.