I don't understand what you think will happen to interest rates.
The government has sold long-term bonds with a fixed interest rate and (usually) repayment date to fund its debt. That interest rate for existing debt will not change.
When it wants more money, it will offer some more bonds. The price paid will depend on the interest rate that the lenders want, and their view of the credit-worthiness of the UK government (and the Scottish government, if independent). The interest rate on these future bonds might be anything. It will reflect world interest rates as well as long-term interest rates inside the UK. It might be index-linked. If it becomes known that the government intends to use inflation to shrink its debt, lenders may insist the loans are denominated in Euros or Remnimbi. A lot of these bonds may be sold to pension funds, to balance their long-term liabilities, though the declining popularity of annuities may shrivel up this demand.
It will also get some money by selling off banks it has bought, or using the Thatcher method of selling to the citizens of the nation those things which the citizens already collectively own, including town halls, civic buildings, psychiatric hospitals, bus companies and publicly owned utilities. For example next time it might sell street lamps, motorways, police stations and more hospitals.