Short answer: no, it won't go through on its own while those two debts are sitting there. A strike off objection can only be lodged by someone with a genuine interest, and the two obvious candidates here are the Bounce Back lender (over the £2,000) and HMRC (over the £4,500 corporation tax). Both routinely object as a matter of policy whenever a DS01 lands and there's money owed. Each objection suspends the process for a set period, and the objector simply renews it when that period runs out. That's almost certainly why it was blocked at the start and again two years on. It's not that Companies House has forgotten about you; the creditors are keeping the company alive so they still have someone to chase.
What this means in practice - The company is still legally in existence, so confirmation statements and accounts are still due. Missing them brings late filing penalties, and Companies House may start its own compulsory strike off, but the creditors can object to that too.
- The BBL is 100% government guaranteed, but the lender has to show it made recovery attempts before claiming on that guarantee. Objecting to a strike off is one of the cheapest ways to do that.
- HMRC will not release a company with unpaid corporation tax and will keep objecting indefinitely.
Realistic ways forward The cleanest route is to clear the £2,000 with the lender, then contact HMRC about the corporation tax. If the company has no funds, HMRC can be asked to accept that the debt is uncollectable, though they may still want the final return and accounts filed before they stand aside. Once both withdraw their objections, a fresh DS01 should go through in a couple of months.
One point worth being careful about: if the company had cash that went to you as a shareholder or director while the tax and loan were unpaid, that can be looked at even after dissolution under the 2021 dissolved companies legislation. Your state pension has no bearing on any of this; the debts belong to the company, not you, unless personal guarantees or misconduct are involved.
If the numbers don't add up to settle, a chat with a licensed insolvency practitioner about a low cost voluntary liquidation is worth having. That closes the company properly and the creditors cannot object to it.