Early spring is the best time for London and the English countryside because the crowds are thin, the daffodils are up in the Cotswolds, and airfare hasn't hit those brutal summer peak prices yet. You get crisp mornings for walking through the British Museum and quiet afternoons at a village pub with a fireplace.
A trip like this usually runs about $3600 total for flights, trains, and a mix of city hotels and country inns. Since you're dropping that kind of cash all at once, you need a solid plan to handle the payments without wrecking your monthly budget.
Remember that the 0% intro APR for 15 months on purchases and balance transfers is a deadline, not free money. If you still have a balance left when those 15 months run out, interest will kick in on whatever is left over.