Other things being equal, a downgra

Other things being equal, a downgrade can mean higher borrowing costs. But this time other things are not equal at all.
Since the event which led to the downgrade - the referendum - those costs have gone down.
The risk associated with UK government debt or bonds might in some sense be a little higher than before, but they are still seen as a safe investment compared with other assets.
In a situation where investors have become more reluctant to hold risky assets they buy safer ones including government bonds and that tends to lower the interest rate the government has to pay when it next goes to the market to borrow.
And then there is the increased chance that the Bank of England will reduce its own interest rates because of concerns about the economic impact of Brexit. That tends to push government borrowing costs in the same direction.