There is an important distinction to draw first, because it decides which appeal route is even available to you: a late filing penalty for company accounts comes from Companies House, not HMRC. "Reasonable excuse" is an HMRC concept; Companies House runs a separate appeal process with its own (much narrower) rules.
If the penalty is from Companies House (accounts)
For a private limited company the penalties are fixed: GBP 150 for up to a month late, GBP 375 for 1 to 3 months, GBP 750 for 3 to 6 months, and GBP 1,500 beyond that, doubling if you are late two years running. Only a few days late means a GBP 150 penalty.
You can appeal a Companies House penalty, but the bar is high. You must give a specific reason with dates and times and prove the circumstances were out of your control, for example a fire that destroyed your records. Companies House publishes a list of reasons that are unlikely to succeed, and "it was my accountant's (or anybody else's) fault" is explicitly on it. So your previous accountant going quiet is, bluntly, a very weak ground.
A family emergency is not on that list, which helps: if it genuinely prevented you from filing and was out of your control, it is arguable. But a delay of only a few days is a harder sell, because the expectation is that directors file in time and the penalty is automatic.
The process: write to Companies House with your specific reasons and evidence, and wait for their decision. They will not collect the penalty while your appeal is being considered. If the appeal is rejected, you can escalate to the senior casework manager, then to the independent adjudicators, and finally to the Registrar of Companies.
If the penalty is from HMRC (tax return, VAT, Self Assessment)
Here "reasonable excuse" does apply. HMRC says a reasonable excuse is something that stopped you meeting a tax obligation for a valid reason. Examples they give include: the death of a partner or close relative shortly before the deadline, an unexpected hospital stay, a serious or life-threatening illness, computer or software failure while preparing the return, problems with HMRC's online services, fire, flood or theft, unpredictable postal delays, disability or mental illness related delays, misunderstanding your legal obligation, or relying on someone else to file for you and them failing to do so.
What will not count: not having enough money, finding the online system too difficult, not receiving a reminder, or making a mistake on the return. And whatever the excuse, you must file or pay as soon as you are able.
The process for HMRC is an appeal within the deadline stated on the penalty notice, either through the online form or by letter, with your evidence attached. If HMRC rejects the appeal, you can ask for an independent review or take it to the tax tribunal.
Is it worth appealing?
An honest assessment: at only a few days late the penalty is GBP 150, and your strongest fact is the family emergency, not the accountant. If the emergency genuinely made filing impossible and you can evidence it, an appeal to Companies House is worth the letter; you have little to lose since collection is paused during the appeal. The accountant's silence is not a ground that will carry it. And for the future, the biggest protection is filing early next year, which you are already doing.
This is general information rather than advice on your specific circumstances; the details matter, so keep everything documented with dates.
