I have seen on here a few times that a 13A double socket can't handle 26A but I have failed to find any manufactures who include that in their spec sheets. And I am inclined to think it is some more miss-information. This happens all the time I had a big argument with my daughter who got these silly things one can stick into sockets.
and until some one can point me to manufactures statement that their sockets can't handle two 13A items I will not believe it.
As to overload by having too many sockets at one end of ring main I did try to calculate how close to one end they would need to be and I very quickly realised it is very unlikely to happen.
However what is a problem is the grid switches used to feed washing machine, tumble dryer etc. Are rated at 20 amp so there is an issue here when fitting double sockets. The grid switches can also take fuse holders or can be feed with 20A radials from consumer unit.
I do recommend grid switches on supply to washing machine. If you have ever seen one where the weights have become lose you would realise why. If that happens without a grid switch only way is to switch off at consumer unit as far too dangerous to put hands near washing machine.
I think it is the 20A switch which has started the rumour about about the sockets and it has been changed slightly in the telling.
So if using Grid switch then yes two sockets are required.
As to loading a ring main is normally 32A and Dishwasher, Washing Machine, Oven, Tumble dryer, and kettle are all near the 13A limit so if any of these can be given their own supply it will reduce the total load on the kitchen ring.
A radial is normally 20A and to feed single sockets for Oven (Not Hob as that is well over 13A) Fridge, Freezer, Washing Machine, etc. will help.
There is some disagreement as to Fridge, Freezer some say to put on their own supply could me you would not notice if the supply tripped until too late, others point out it is a lot less likely to trip in first case. I know a friend of mine put them with the intruder alarm as when power to that trips it starts a sounder so unlikely to not notice when tripped.
But unless RCBO's are used that would not help anyway.
So I would suggest you talk to who is doing the job and get advice from someone on site which is far better than asking anyone remote from the job.
Maybe they are using Ali-tube cable and naming the Fridge, Freezer sockets. There are so many options I could write 5 or 6 pages and still miss out bits. So ask the guy doing the Part P cert and see what he thinks.
Missed slash out on img so corrected