For a small window like that I'd budget half a day's labour plus materials. £400-500 all in is about right depending on your area. The lintel swap is the bit that takes the time, not the brickwork itself.
If the existing lintel is rotten, definitely replace it rather than just bricking over the top. It'll only cause problems down the line if you leave it.
Too far to travel for me, the 3/400 quotes are about right for a short days work, but i would not need a lintel to brick up a window, as the above post (from a builder) suggested, the brick kinda support themselves
The price can vary a lot on a job like this one. Most of the medium sized firms I've worked for would be into 4 figures to do the whole job of removing the frame, soldier course and closers, bricking up and colour matching the weather struck and cut pointing.
The OP seems to be happy to remove the frame and just cut out the headers himself leaving the soldier in, so it would work out cheaper.
Agree there's no need for a new lintel. If there's a rotten timber one behind the soldier course, it could be removed and the brickwork taken up to fill in.
It looks to me like it's probably 9 inch brickwork, so in the region of 150 or so bricks.
I've just put it up to £500 a day since you've been making your mind up woody. The war in Iran has sent the price of brickwork rocketing up. Might be £600 tomorrow.
If you need to find a tradesperson to get your job done, please try our local search below,
or if you are doing it yourself you can find suppliers local to you.
Select the supplier or trade you require, enter your location to begin your search.
Please select a service and enter a location to continue...
Are you a trade or supplier? You can create your listing free at DIYnot Local