Does it matter which spelling you use? I am English and my word spell check is forever telling me to correct to the American version. My story is based in England but have been advised there is no reason why I shouldn't approach American agents. I hope I wouldn't have to edit the whole book for different queries. Do agents have a preference?
I'm not an agent and have never been published, so this is just thinking out loud: You're English, it's set in England - so I don't think any american agents would be that shocked to see English spelling. If they really thought the audience would mind that could be edited later, but I'd be surprise if that actually happened (though I'm neither from England or America, so what do I know) but the problem would be the same if you wrote with American spelling and tried to sell it of at the English market. I think both would work just as well but since I'd assume you'd be more likely to be published in England I'd advice on English spelling. Or which ever you're more comfortable with, I guess. As far as your spell check you could probably change it in to English spelling.
CHAPTER 1 dr1 Mommy always said I was mid-Atlantic. Or conceived at sea, at least. The consequence for my prose was the blur of ill-fitting colors on a screen, the flickering programmes of an aluminum hue, my mind at once Yankee and tea cup...
Just stick with English spelling. Change your spellchecker on Word to British English lol and save yourself the headache. The important thing is being consistent. Don't use British English one moment and then American English the next. And since you're not American, unless there's good reason to use American English, I just wouldn't do it. There're probably nuances in the language as well as slang etc that you just won't know about unless you've actively paid attention to it, which likely you have not. I've heard of Brits and Americans misunderstanding each other constantly due to differences in culture - the same language is interpreted differently sometimes. Basically, save yourself the trouble. If your publisher wants to edit the book to suit an American audience, they'll do it for you, if it really mattered.
My understanding is that you need to edit the spelling and some of the narrative phrasing (boys and men aren't going to wear "jumpers" in a book aimed at Americans, for example) for the market you're published in. Whether you have to edit it for the agent you're querying, I don't know; I'd be inclined to think yes, but I don't know. I would think that a large percentage of the editing would be search and replace.
I don't know what the rules are in publishing, but there is a fantasy series I read by Scott Lynch where spellings were changed for the UK release, 'Gray King' to 'Grey King' etc. I don't know if the author had to this personally or if the publishers did, but it is something that can happen. That said, there have been other American novels I've read that haven't changed the spelling and it doesn't trip you up as long as it makes sense in the story - I would probably find it odd if a story I was reading set in England with English characters used American spelling. I agree with @Lemie , if it's set in England it makes more sense to me to use English spelling unless told otherwise and vice versa.