You can remortgage but typically if its outside the fixed term of the loan there will be hefty pre-payment fees. So if you get a 2 year fixed interest rate and then try to remortgage within a few months, you will be charged a penalty of circa 3% of the outstanding mortgage.
Not sure if there are any that are at 5% deposit. HSBC has a lifetime tracker that has no repayment fees but the LTV is lower.
Could you afford to stick with the interest rate for a 5% deposit for 2 years? You might be surprised how long refitting your home takes. 6 months to a year for a place that needs a lot of work is probably more realistic.
We were advised to do exactly this when considering a fix it up that would have needed an extension. IIRC it was a minimum of 10% for a lifetime tracker product that wouldn't attract penalties when we remortgaged.
We went for a different house in the end but not because of the mortgage issue.
One of the formal obligations of a lawyer dealing with a mortgage is they have to report to the bank if the borrower has owned it for less than 6 months. Many lenders will subsequently refuse to lend. There are specialist lenders or specialist products but be careful, your options will be fairly limited (and possibly expensive) if you look to remortgage so quickly.
The other thing to bear in mind is that cosmetic changes, even new fittings etc might not necessarily add value to the house, check with professionals first.
There are ways to do it but you need to do your sums and your homework v carefully. Good luck.
The other thing to bear in mind is that on the figures you have quoted above, there is no equity release when you remortgage.
If you buy at £180, 000 and borrow £171, 000 you will pay a fairly high rate because its a 95% mortgage. If you do some work and the house is then worth £200, 000, and you remortgage for £170, 000, you'll get a better rate (probably) because its now only a 85% mortgage.
But the remortgage amount is the same as the original loan - you get £170, 000 from the re-mortgage to repay the original £170, 000 you already owe. You wont get any extra money, or any equity release.
Your monthly payments will go down though.
Sorry if you already knew that but it sounded like you thought you'd get a lump sum from the remortgage.