If it was a few years ago then you can just open another ISA account with another brokerage. Your £20k ISA allowance resets on the 6th of April every year. So unless you’ve paid into your existing account since the 6th of April, you can just open a new stocks & shares ISA account. I personally have accounts with three different brokerages. HL are pretty good, but the fees are quite high if you trade individual stocks.
You can even cash out of your old account and use it to fund your account for this year. That is fine if you aren’t planning on hitting your £20k limit for this year.
Regarding whether your ETF tracks the broader market, it depends on what your ETF invests in. If it is tracking an index, like the FTSE 100 or S&P 500, then it will broadly track the market. Though those indices obviously have different exposures to various industries and geographic locations.
Unless you know what you’re doing, investing in ETFs with strong track records seems quite sensible. You pay a management fee for somebody else that hopefully knows what they’re doing to pick stocks for you. Just check that the fees are reasonable and that the fund has performed well over a long period of time.