Penalty Fares used to be issued for £20 or twice the undiscounted Anytime (Day) Single regardless of the time or date of travel - whichever was the higher. On the 6th of April 2018, however, the new
Railways (Penalty Fares) Regulations 2018 came into force.
Regulation 9(6) thereof changed the previous regime to it being £20 or twice the "full single fare applicable" (whichever is the higher), with the latter
explicitly taking into account "the day and time of the journey that person is making" (Regulation 9(6)(b)).
It was therefore incorrect for you to have been issued for a Penalty Fare for the amount of £30.20 on a Sunday (which would have been the correct amount for a non-bank holiday weekday, at twice the £15.10 Anytime Day Single). This is because there are
Super Off-Peak Single fares which are valid on weekends and bank holidays, costing just £11.90. The correct amount of the Penalty Fare would therefore have been £23.80.
Regulation 16 sets out how Penalty Fare appeals are handled at the first instance. Regulation 16(3)(a) sets out that one of the valid grounds for an appeal is "the penalty fare was not charged in accordance with the requirements of these Regulations", which is clearly the case where a Penalty Fare has been issued for the incorrect amount. Therefore any appeal you make should be allowed, and in fairness to the appeals body, we have heard of a number of similar cases since the new Regulations came in, where people were issued with a Penalty Fare based on the Anytime fare instead of a cheaper, valid (Super) Off-Peak fare - in each of those cases as far as I'm aware the appeal was allowed.
I would therefore appeal the Penalty Fare using the details provided on the notice, outlining the above as your reason for appeal. You may wish to draft an appeal and then post it here for people to read it through and check that it looks OK. However, since you boarded at a station which undoubtedly had available ticketing facilities (King's Cross), you should be aware that the usual alternative to this matter being resolved by means of a Penalty Fare is for the train company to prosecute an offence committed under Byelaw 18 of the Railway Byelaws. In the particular circumstances of your case, since you boarded with a valid ticket and presumably handed this over for inspection when asked, as far as I can tell, you couldn't be prosecuted under that. You might, however, still be liable for prosecution under another law.
But all of this is to say that, because of the potentially more serious alternatives to having the matter disposed of by way of a Penalty Fare, you should make sure that, in the unlikely event of you submitting an appeal against the Penalty Fare but this
not being responded to by the end of the period where the Penalty Fare is due for payment, you should ensure that you do pay it, to prevent it from being cancelled. Unlike certain other kinds of penalty notices in life (parking charges etc.), payment of a Penalty Fare does
not imply acceptance of guilt, and does not prevent a successful appeal. A paid-up Penalty Fare will be refunded in full if the appeal is successful.
Once 21 days pass from when you submit your appeal, or the appeals body responds to your appeal, the train company can no longer prosecute an incident for which they issued a Penalty Fare. They, equally, cannot pursue an incident in relation to which a Penalty Fare has successfully been appealed. So it is in this window of potentially up to 21 days that a risk exists - if, for example, they cancelled the Penalty Fare for non-payment and initiated a prosecution.