You can only put a travel date of up to exactly 3 months ahead of the date you apply online.
Therefore if you apply on April 9th, you cannot put a travel date of July 12th because that is more than 3 months ahead.
So you either:
- apply on April 9th and put a travel date of July 9th (or earlier)
Or
- apply on April 12th and put a travel date of July 12th
Basically you want to put the EARLIEST possible date you might wish to enter the UK. You don't want to be in a position where you get your visa back in, say, May, and you have changed your mind and want to travel in May, but your visa is not valid until July, meaning you're stuck in the US.
Also, bear in mind that they don't always honour the intended travel date and sometimes make it earlier than you want. You might ask for July but find it actually starts in May instead. So, if it HAS to be a July start date because of your timings, make it VERY clear on your application that you do not want it to start until July.
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