Can I travel on the current uk visa I have?

No it will not create any problems. It often happens that students need to postpone their entry for a semester since they did not apply for their visa early enough. The new confirmation of acceptance for studies will not create any problems either as long as the sponsor whose license number is endorsed on the visa is the same. Just make sure that you carry the same documentation that you have used for the visa application in your carry-on baggage so that you can present it to the U.K. Immigration Officer on entry..