The lender is introducing a five-year fix at 3.39% available up to 75% LTV with an arrangement fee of £100 and a completion fee of £695.
It is also launching a two-year fix at 2.59% available up to 75% LTV with an arrangement fee of £295 and a completion fee of £695.
Both products have a maximum loan size of £300,000.
Chris White, chief executive of Hinckley & Rugby, says: “We are expecting a lot of interest in these very attractive rates from borrowers and those remortgaging who want the reassurance of a low-priced fix.
“At a fixed interest rate of just 3.39% this is a winning combination for many in the market today, who want to be able to plan their repayments for five years with certainty.”