To expand further on your scenario.
Current mortgage 145,000 at 4.55% interest over 20 years
Repayments, say, £ 915, total repayable £ 219,370, interest paid £ 74,370.
If the whole amount was re mortgaged then you must allow for the interest on the original amount and loan amount separately not all together.
Option A.
Re mortgage £155,000.
£145,000 allocated to original loan, £10,000 new loan.
145,000 @ 7.55% interest over 25 years = repayments £1,053.00, total £315,843 interest paid £ 170.843.
10,000 @ 7.55% interest over 25 years = repayments £73, total £21.783 interest paid £11,783.
Option B.
Secured loan.
£10,000 at 18% interest over 10 years.
Repayments £172.00, total repayable £20,603, interest paid £10,603.
So going off your scenario the secured loan whilst at a higher interest rate over a shorter term is the preferred option.
Option C.
However, if you can get a second mortgage to run alongside your original mortgage for a 10 year period, even if the interest rate is slightly higher than your original mortgage then that would still be a cheaper option.
Current mortgage 145,000 at 4.55% interest over 20 years
Repayments, say, £ 915, total repayable £ 219,370, interest paid £ 74,370.
Second mortgage £10,000 at, say, 10% interest over 10 years
Repayments £130.00, total repayable £15,574.00, interest paid £ 5,574.00.