I have seen it mentioned somewhere that there must be at least 2 shareholders left after the share buyback. In your case, apparently there will be only one shareholder left. You should recheck this provision before you proceed.
I believe that Auditor's Report (s 173(5) CA 1985, completion of Form G173 and notice in London Gazette and newspaper are only required if the share buyback is out of capital as opposed to out of distributable profits.
Subject to first paragraph above, I believe that you only require to comply with the following:
(1) Ensure that articles of association must authorise the repurchase. Table A of Companies Act 1985 apparently includes this at para 35.
(2) Shares to be repurchased must be fully paid up.
(3) Consideration from the company must be paid when sale occurs
(4) There must be irredeemable shares in issue, held by at least two persons, after the repurchase has taken place.
(5) There must be a shareholder approval of the proposed contract for repurchase. Such approval must be by a special resolution at an extraordinary general meeting of the company.
(6) Special Resolution must be filed with Registrar of Companies within 15 days of the meeting.
(7) The company must complete form G169, have it stamped at 0.5% of the repurchase price and send to Companies House within 28 days of the repurchase.
(8) Notify Board of H M Revenue & Customs of the repurchase immediately after the execution of the contract and to retain the contract for 10 years.
(9) S 219 ICTA 1988 must be complied with to secure CGT treatment. This states that the company must be an unquoted trading company, purchase must be made wholly or mainly for the purpose of benefiting a trade carried on by the company and the purchase must not form part of a scheme or arrangement, one of the main purpose of which is to enable the vendor to participate in the profits of the company without receiving a dividend or the avoidance of tax. You could apply to secure advance clearance under S 225(1) ICTA 1988 from the board of H M Revenue & Customs.
I hope this helps.