I'm also a contractor.
For us, the advantage of an offset mortgage is that you can keep access to your savings in case of lean times for business, while also reducing your mortgage payments. This gives you the benefits of overpaying without actually parting with the money.
That might be worth paying a premium for an offset, but it depends on how you trade and what your income is. If you use a PAYE umbrella or are employed on fixed term employment contracts, it might be worth it, as your "warchest" will be part of your personal finances. If you trade using your own limited company, then it's better by far to keep your "warchest" inside the limited, especially if drawing that money instead would put you into the higher rate tax band. By leaving it in the company until you need it, you defer the income tax until the year you actually draw the money.
Another factor to consider when deciding whether to overpay on a mortgage, especially if you are under 40, is the lost opportunity to instead invest that money in a pension. Pension contributions are (subject to contribution limits), tax free. This make a huge difference to their ROI compared with any investment made from taxable income, especially when your income would otherwise exceed the higher rate tax threshold. Because of compounding, a relatively modest return on that investment of 5% per year turns £1000 into £3207 after 20 years. Compared against the saving you make by overpaying on what is probably the cheapest loan you'll ever have, it's a no brainer IMO, as long as you're happy with the risk.
Counter intuitive though it may sound, if you are paying higher rate tax and wanted to buy a car or something similar, it would be more cost effective by far to borrow that money at a low rate of interest and make repayments from income in the basic rate band, than it would be to pay cash from income you'd paid 40% tax on. I guess that's the difference between debt and leverage.
Everyones particular circumstances, objectives and attitude to risk are different though, so there is no cookie cutter answer here. Spending a few hundred to discuss your circumstances and attitude to risk with an IFA would almost certainly be a wise investment. Also, have a look at the contractor uk forums, there are plenty of folks on there that will help with questions like these.