@Julie *********
You should apply for a 60-days single entry Tourist Visa in the online E-visa system of the Royal Thai Embassy London.
Register online and start with the visa application step by step. When you finish each page, click the button in the corner that says “save” and your info is saved in the system.
(NOTICE: They are down for maintenance of the system at the moment, so you will receive 404 not available messages)
You enter Thailand with this visa and will be stamped in for a 60-days stay permit.
You can extend the stay permit ONCE on Immigration for 1900.- THB for 30 more days. Bringing your possible stay in Thailand to 90 days.
ATTENTION when booking the flight: The day you arrive is counted as day number one.
So you need to watch out you don’t book your flight with a departure date 91 days after entry – this would mean you are on “overstay” and this is not recommended.
The London Embassy maybe will ask you to upload a flight out of Thailand within the 60 days the visa gets you stamped in – I actually are not sure.
In this case they will inform you by email and ask you for such a proof.