Shipping times from over-seas can be very good with the right courier, at the moment were using EMS speed post and there delivery time from Singapore is 3 days. Which I'm sure wouldn't be a problem for your customers.
Like what was said above if there were any problems with the product returning it would be a long and stressful procedure if your products were sourced outside of the UK.
VAT and import duties make dropshipping to eBay customers a problem. However many times you put in your item description that "you may be charged import duties" etc. there will always be the people that leave you negative feedback and won't budge. This is unless you can offer prices around 30% cheaper than your competition.
I'd look for a UK dropshipper and when you have a little more cash start buying in bulk, it will be more profitable in the long run and may not require very much money.