As far as I know, EY has training batches commencing always on a Sunday, 2-3 times a month perhaps. They told me they need 13 people to make a batch, although I'm not sure if that was an exact number or a minimum requirement..? In any case then, training dates are a common occurrence, so worry not!
To help things along, try and be as flexible as you can with your requested date/s of joining, as it makes things easier on their side if you have a wider time frame to work within.
As for your current employer.. do you legally have to give that much notice? I thought the normal tender was one month only? If someone has asked you to work longer than what is stated in your contract then I think you have the right to refuse...