You're right on the three main items, and yes, there are strict deadlines. Here's the full checklist for issuing shares to your investor.
1. Shareholder authority first. Check your articles of association. Unless pre-emption rights have already been disapplied, existing shareholders must be offered the new shares first - which is awkward when you're bringing in an outside investor. Companies normally pass a special resolution to disapply pre-emption rights and authorise the directors to allot the shares. Document this with board minutes and the resolution; it's the legal authority for the whole issue.
2. File form SH01 with Companies House. The return of allotment must reach Companies House within one month of the allotment date - that is the strict statutory deadline (GOV.UK: 'within a month if you issue more shares in your company'). File it online through the Companies House service; it's much quicker than paper and you usually get same-day confirmation. If it goes in late, Companies House can reject the filing and the company and its officers face penalties, so I'd file it on or before the day the money lands.
3. PSC register. A person with significant control is someone with more than 25% of the shares or voting rights, so a 15% angel won't normally be a PSC - unless they also get rights such as appointing or removing a majority of directors, or exercising significant influence or control. If nothing changes on the PSC front, there's nothing to file; if PSC details do change, Companies House must be told within 14 days.
4. Share certificate. Issue a certificate to the investor showing the company name, investor name, number and class of shares, and amount paid up.
Finally, update your statutory books - register of members and register of allotments - and reflect the new share capital in your next confirmation statement. Practical tip: complete the paperwork on the allotment date itself, not when the money arrives, because the one-month clock runs from allotment.
