[I waffled on a bit below. The short version is that you shouldn’t need to worry about changing your quotation marks for the UK unless this is explicitly stated as a requirement by particular agents, because we use double speech marks in the UK anyway. Many publishers just use single quotes as a matter of house style, it seems.]
There is no easy way to do this (for the very reasons your surmise), but I wouldn’t recommend doing it either - unless you know it is required by the people to whom you are submitting. The way we use quotation marks over here (I’m British) is somewhat odd - the only time we ever see single quotes used for dialogue (or double quotes for quotes within quotes) is in published books such as novels - and even then, it’s not all of them (although it is the majority of UK-published books). Ultimately, it seems to be a matter of house style.
However, I don’t know anyone who actually writes using single quotes (although no doubt someone here does!). Learning to write in the 70s and 80s, I was taught to use double quotes for speech at school. When I was a primary teacher in the 2000s, I likewise taught children to use double quotes. (Here you can see a government document on punctuation taught in the National Curriculum, in which the example of speech marks - The conductor shouted, “Sit down!” - uses double quotation marks.) When we type, we use double quotes for dialogue. Every essay I wrote at the universities I attended used double quotes for speech.
In fact, I’ve always been curious about why some publishers use single quotation marks. It seems that the Oxford Dictionaries website (which you would think would be definitive) and several others state that it is convention to use single quotes in English written work, and yet, as I say, it’s not a convention I’ve ever seen used outside of published books. (And if you do a search on the 1813 edition of Pride and Prejudice - published in London - you’ll see it uses double quotes, as did Jane Austen in her handwritten manuscript. So it’s you Americans - assuming you are American - who are correct in your speech mark usage and British publishers who have done something weird.)
My English teacher in high school told me that the only reason single quotes are used in published books was to save ink during the war - I doubt this is true, as I’ve never found any evidence for it (aside from one claim online about it being down to an 1812 blockade). According to Wikipedia, the single quotation mark is newer anyway, and only evolved as a way of indicating secondary quotes within the double quotes. (Wikipedia also seems to suggest that our tendency to use single quotation marks only dates back to the 1960s.)
Take a look at some British newspapers, though:
guardian.co.uk
thetimes.co.uk
They all use double quotes for speech (although they may use single quotes in headlines).
A random selection of books from my shelves suggests that even publishers switch between different styles in different books. One novel publish in the UK by Vintage uses double quotes, another single quotes; a 1989 edition of Unbearable Lightness of Being by Faber uses double quotes, a 1995 edition by the same publisher uses single quotes. The vast majority certainly use single quotes, but it’s by no means uniform.
As far as I know, everyone over here writes using double quotes and these are changed by the publisher if the publisher’s style is to use single quotes. (My wife is a journalist and had to train herself to use single quotes for one magazine she wrote for, but that was the exception rather than the rule.)
So, unless the UK agents to whom you are submitting explicitly state on their website or elsewhere that they require single quotations for speech, then I would not worry about it. I’m English and if I ever get to a point where I can submit something to an agent, I would use double speech marks too. We are used to reading both types, single and double, and rarely notice it, and nearly always write using double speech marks.
(Apologies for the long reply - it’s a topic I’m interested in!)
All the best,
Keith