I've had a hard time finding out details on remortgaging Help to Buy loans myself, but found one article (http://www.thisismoney.co.uk/money/mortgageshome/article-3038831/Help-Buy-borrowers-risk-missing-best-remortgage-deals.html) which points out it IS possible. But also that there aren't many lenders offering such deals out there. The article lists a number of lenders that do offer these programs, and the extra requirements on equity you might have to have.
It sounds like it's going to be critical to know how much equity you've built up. Since part of the valuation increase will be credited to Help to Buy, you won't get all the £30k increase you've mentioned. Instead, I believe you'll only get 80%, so £24k. Which would mean your total equity is £24k + £7k = £31k, plus whatever you might have already paid off. I'm going to assume there isn't much you've paid off, so will assume just over 18%. (31/170)
While this is higher than most of the equity limits mentioned in the above article, keep in mind you'd only get cash out corresponding to the difference between your current equity amount and the equity required for the loan. For example, if you went with a loan requiring 15% equity to qualify, you'd only have 3% over that, and thus get £5.1k out. And that's before any fees you might have to pay! (You might have new origination fees, but you also might have early repayment fees.)
Maybe you could pursue a lower money down refi and get to keep more, but the same article points out that Help to Buy might consider that too risky for you, and refuse to allow the refi.
I think it's worth shopping around to get actual numbers for your exact situation, but personally it doesn't sound like you have enough equity yet to get much cash out of a refi. Perhaps you'll get lucky though. Best of luck!