There are two separate parts to this (1) Britain's elected leaders wanting not to be a part of a TTIP-like agreement and (2) Britain's ability to negotiate a better deal outside of the framework of the EU.
Desire to avoid TTIP
Currently one of the biggest supporters of TTIP in the EU is the British government itself, Prime Minister David Cameron has pledged to put "rocket boosters" behind plans.
Certainly there is little evidence that the political will is against the content of the agreement as it stands. There is no evidence to suggest that such a position is likely to change with the present government.
Negotiation as an EU member state
There has been some concern that the EU member states could not exercise their veto in the way they could for the ACTA agreement, though I believe this is no longer the case (corrections welcomed in the comments.)
The British government has indicated that there is an NHS Exception in the negotiations and there would be insurmountable pressure to use it if that exception not the case, not least of which because the NHS employs 1.5 million people who would be inclined to vote differently at the next election.
The ΣΥΡΙΖΑ / Syriza government in Greece say they will never ratify TTIP.
The French government have been asking for a cultural exception to protect French Cinema from Hollywood; and more importantly will not accept harmonisation in Food Safety and Agricultural rules which are perceived to benefit American interests.
“We will never accept questioning essential principles for our agriculture, our culture and for the reciprocity of access to public [procurement] markets,” Hollande is reported as saying at a meeting of left-wing politicians in Paris. “At this stage [of the talks] France says ‘No.'”
Source: Independent, 3rd May, 2016
This leaves the possibility of TTIP happening at all rather remote at best.
Negotiation outside of the EU
Once informing the European Council of an intent to leave, Britain has 2 years to negotiate a viable trade agreement. Given the glacial timeframes of EU politics combined with bad feeling and a desire to "stick it to Britain" for affecting the stability of the union this is unlikely.
To avoid TTIP a bilateral trade deal that specifically exempted the country would be required because a fall-back to WTO tariffs on import/exports would harm both UK and EU trade; and while Britain could rejoin the EFTA (including Norway, Iceland and Switzerland), they are fully expecting to get TTIP 'through the back door' saying...
Since the EEA EFTA States are closely integrated in the EU’s Single Market through the EEA Agreement and therefore apply the same Single Market rules, any impact that TTIP may have on the Single Market is likely to affect the EEA EFTA States.
Source: EEA Joint Parliamentary Committee adopts resolution on TTIP
The EEA EFTA relationship with the EU could be summarised as "You say, We pay" and with no real input or protection for EFTA members in the TTIP or any other negotiations the EU might do with India or China.
Some temporary measures could give extra time to negotiate an EU deal (the remaining EU members ALL permitting), trade deals take a long time to complete, for example:-
- The CETA EU/Canada deal has recently been ratified following 7 years of negotiations. It is considered quite a quick result and was conducted on good terms.
- A similar India/EU deal is not yet complete was considered 'almost complete' in 2011 and in the final lap in spring 2013 but is as-yet incomplete in 2016. Talks began in 2006.
In any case it would be obvious to any other potential trade partner that, without a good EU trade deal, they would be more necessary to the UK than the UK is to them. This places the relatively large market of the UK in a weak bargaining position and leave the British negotiators in the position of having to accept any trade deal available - even a bad one for the UK.
