I hope you have better luck than I had. I took the car back about a month later specifically to have the R33 thing seen to, and sat for about three hours in their waiting room, to be told that the technician was unable to do it because the system kept trying to update from R21 instead of from R13 and he was afraid to take a guess at what to do in case he bricked the car. He would get advice from MG and get back to me.
Weeks and weeks passed and it took another furious email to get any action. Then I got a call back and yes they could book the car in to do this, and the undertray fix which they graciously conceded had become available - that was the other main topic of the shouting-match - at the same time. On 10th September. This all started in the middle of April.
I'm beginning to think I'm the only person in the country who is still on R13. I've been complaining about aspects of it since I got the freaking car. They have plenty documentation. I nearly rang them up and demanded the update when it first became available late last year, but thought I could wait till the first service. But then - "we only do these updates if the customer complains about something" was the first excuse. When I asked them rather pointedly how many more complaints they'd like, they started with other excuses.
If it's not sorted next week I will get positively homicidal. If it is sorted, I'll wash my hands of them and go to a different dealer.