[I'm assuming your shares are US domiciled and you are subject to US / LPR taxes]
I know nothing about investment clubs either. A cursory glances suggests HMRC's idea of what an investment club is is very different to US ones. In case I'm wrong, here's a link to HMRC help page on capital gains/losses from investment clubs:
https://www.gov.uk/tax-sell-shares/investment-clubsWhat I actually came here to say was be very careful about the timing of your return to the UK (apologies if you already know this). The rules for which year you become UK tax resident depend on a number of factors and are too long to sum up here (Goggle 'Statutory Residence Test' for more info). If you're not careful, you may be considered to be tax resident (and therefore subject to UK taxes)
before you physically arrive in the UK. Even then, you may qualify for split-year treatment, but IMHO we're already well into 'you need a professional tax advisor' territory by then. On the other hand, if you come late in the UK tax year, it's also possible you won't be UK tax resident until the following April 6th. That can be advantageous if you are coming from a US state that has a capital gains tax (42 of them do, plus WA starts Jan 1st next year) as there is a window where you can sell while only covered by US federal taxes.
From you post you're expect to receive stock in a company. Just for completeness, if the shares from the investment club are not simple stocks (e.g. are Mutual funds or ETFs), you'll almost certainly need to dispose of them before returning to the UK else you'll pay income tax rather than capital gains tax on your gains (Google 'uk taxation of offshore funds'). Vanguard does a line of ETFs (VOO etc) that are both US & UK friendly if you're looking for equivalent funds.
The US calculates capital gains on the price you buy and sell specific shares at. The UK works on an average cost basis. If the shares were purchased over a period of time by the investment club, they may have varying cost basis's. Since 2011, US brokerages have had a legal obligation to record cost basis so if all else fails, you should be able to look it up after the investment club sends you the shares. The UK cost basis will be cost basis of anything you haven't sold by the time you become UK tax resident. If you aren't planning to sell all the shares at once, pay attention to which share lots you sell as otherwise the FTC (Foreign Tax Credit) from one country won't match the tax bill from the other.
Given the UK 20% GCT band kicks in at about $53k ($69k with allowance) vs the US's $445k (filing single), you may want to look into selling your stock and repurchasing in order to reset the cost basis before moving to the UK.
At large numbers, taxation of capital gains is actually slightly lower in the UK that the US (thanks to NIIT - Net Investment Income Tax that kicks in at $200,000). Note you can't claim NIIT back against your UK taxes.
Finally, if you've not already read this advise elsewhere, make sure you shares are in a brokerage that doesn't close the account when they find out you're no longer living in the US. If you can keep a US bank account, that is also a really good idea as getting money to/from the government / brokers can be difficult without one.