Transfer to the EUR account:
As our client money account is held with Barclays Bank Plc in London, UK, BUT in EURO usually it should be enough to create a EUR transfer providing just the IBAN and, in some cases, the BIC. Since it's an intra-EU transfer in Euros your bank shouldn't charge you more for this than for a normal EUR transfer. At least not in theory as the EU Payment Services Directive should prohibit your bank from doing so.
Transfer to the USD account:
All funds that you transfer from your GBP or EUR bank account to your USD account will be converted into USD by our bank.
However, our bank applies a 2% charge on the exchange rate conversion, which may or may not be better than what you can get elsewhere.
We suggest that you look into alternatives before sending us money in a currency that's different to the currency of the goal you are funding.
A number of clients use Transferwise for this very reason. If you sign up via https://transferwise.com the first transfer (up to GBP 500) is free of charge. (Disclosure: We get 50 GBP commission for every three clients that sign up via this link.)