People here in the UK want to pay in GBP (British pounds), as otherwise our banks gouge us on the transaction(s), with terrible exchange rates and fees.
If you can, use a payment processor that will allow people to pay in their native currency, especially if it is a relatively small amount, or the fees and loss on the exchange rate may be more than your cost, which is annoying.
you should do it.
I have programmed such a software myself for a customer of mine. There is definitely space for this. our program was not web based, it was java swing. Times has changed, I can imagine there is a good deal of interest in it.
But have in mind, UK people don't have euros. They still have their pounds.
Euros are for the rest of europe. And this includes germany, which is probably a huge market for your tool.
Yes, for sure, offer it in UK and Europe, use their currency if you can, it looks better from their point of view ... but don't stress, people are becoming used to USD as a defacto standard.
NOTE: You want to do a GBP not EUROs for England, while they are a member of the EU, they opted out of the Economic and Monetary bit
You may not be able to do a direct USD to translation and expect to be able to charge that. Your going to have to look at what is a suitable equivalent price per country. For EU and England you are in a better position given the US dollar at the moment. Coming to Australia could a different story though.
Certainly wouldn't hurt to enable payments in non-USD currencies. Our merchants can accept payments in Euros, Pounds, USD, AUD, CAD, and Yen, and their order pages are translated into 18 languages. Given the direction you're headed, you may want to take a look at or possibly speak with the folks at mindbodyonline.com, who have been SaaS servicing the training/gym industry successfully for a while. Nice guys.