Unfortunately, you have to be "resident" in the UK for 6 months (more than 185 days) before you can apply for a provisional license. x
http://www.direct.gov.uk/en/Motoring/Motoringtransactions/BeforeyouapplyC/DG_10035602
There has been some debate about this in the past. I'm of the opinion that you can apply for the provisional at any time because fiance visa holders are considered to be 'normally resident' in the UK.
From the link:
A provisional driving licence is issued in order to enable a driver to take a driving test. To apply for a provisional driving licence, you must therefore be 'normally resident' in the UK for more than 185 days.
I don't think this means you have to
have been in the UK for more than 185 days before you can apply (it says 'must
be normally resident for more than 185 days, not 'must
have been resident for more than 185 days')... which I take to mean that you need to be in the UK on a visa giving you permission to live in the UK for more than 6 months -which is the same as for NHS treatment.
The fiance visa is a bit of an anomaly, because even though it is only valid 6 months, it is a settlement visa, and leads to FLR(M) and then ILR - and with a fiance visa you can use the NHS immediately without having to wait 6 months.
In contrast, it also says that EEA citizens specifically cannot apply for their provisional licence until they
have been resident in the UK for 185 days:
EU/EEA drivers who wish to pass a first test, or gain additional entitlement, must be normally resident in the UK. Drivers who have moved to the UK having been permanently resident in another state of the EU/EEA must normally have been resident in the UK for 185 days in the 12 months prior to the application for a driving test and a full licence. Normal residence means the place where an individual resides because of personal and/or occupational ties.
Someone on a fiance visa is considered to be 'normally resident' in the UK (it is their main residence and they intend to live in the UK indefinitely)... so they should be able to apply for a provisional licence whenever they want to.