Speedbird252, As an instructor/examiner I am amazed that you were caught out by considering flying through the Odiham ATZ at an altitude of 2300 feet. I am not blaming you, as I would not expect you as a student to necessarily have picked up on the fact that Odiham has an airfield elevation of 405 feet AMSL, since there is so much information to be extracted from the chart that it is easy to overlook some detail.
However I would have expected your instructor, whilst briefing you for the flight, to have ensured that you either planned to fly high enough to be above the Odiham ATZ or to plan to miss the ATZ completely. Whilst any altitude above 2405 feet keeps you out of the Odiham ATZ there is a further gotcha at Odiham – they wire tow to 3000 feet AMSL! Perhaps a better option would have been to plan Whitchurch-Farnborough-Guildford. This would have overcome the problems with the Odiham ATZ, kept you further away from the gliders at Lasham and since you were talking to Farnborough they could have provided clearance through their ATZ, if required, whilst ensuring that you did not conflict with their inbound/outbound traffic.