OK, that plug is ...
interior diameter: 2.5 mm external diameter: 5.5 mm and in this application is required to reliably carry 3Amps.
From your picture looks like a long shaft - 14mm do?
Order Code HH63T at Maplin, 99 pence.
Free delivery up to this Tuesday, or your local shop.
- then it's a soldering iron job if up to it...