The procedure for a British person wanting to get married in Thailand is
detailed on this webpage. There you will see the need to go to the British Embassy in Bangkok, having previously prepared your affirmation document, sign it there, in front of a designated embassy official, then go back the next day to pick it up, then get it (and if you have been married before, also your previous spouse's death certificate, or the Divorce Decree Absolute) translated into Thai, then go to the Thai Ministry of Foreign Affairs to get that translation certified.
Once it bears the official stamp of the Ministry you can use those documents, and your passport, which is detailed in the affirmation document, to get married at any Amphur (Register Office) in Thailand. No appointment needed.
But for you, you are not marrying a Thai, so your fiancée needs to go through the same procedure, except she will not go to the British Embassy ... she will instead go to the Vietnamese Embassy to sign her affirmation document. Then same procedure applies ... translation into Thai ... take to Ministry.
The additional hurdle for you two is that, I presume, neither of you speaks Thai, so the Amphur is unlikely to agree to register your marriage unless they are certain you understand the nature of what you are just about to enter into. So you would be well advised to take someone from a translation bureau along with you when you go to the Amphur.
Registering the marriage? A simple form-filling procedure .... fill in a form and produce evidence, for you and your fiancée your respective affirmations stamped by the Ministry, and passports, pay a small fee,and then you get handed two copies of the marriage certificate.
How long does it all take? Firstly I say, don't even think about it while much of Bangkok is under water. There is much disruption at the moment. But once it is dry again, is a week long enough? Quite possibly.
As regards "appharently it takes 2 days to get the Affidavid of single status issued by the Vietnemese Embassy in BK", do make quite sure exactly what their requirements are. By that I mean this. Whilst the British Embassy is quite prepared to countersign any affirmation presented to them, as necessary with supporting documents about previous marriage, for example, the Danish Embassy is not prepared to countersign unless the Danish Citizen has obtained a CNI from a Register Office in Denmark. So there is a suspicion in my mind that the Vietnamese Embassy in Bangkok might have the same procedure, given that for a marriage in Vietnam you have already made clear a CNI is required for a non-Vietnamese person wanting to get married in Vietnam. Your fiancée needs to make quite sure! If she has not already done so she should have a look at .....
http://www.vietnamembassy-thailand.org/vi/ , and as necessary even phone them?