BS7671:2008 said:
The load current in any part of the circuit should be unlikely to exceed for long periods the current-carrying capacity of the cable (Regulation
433.1.5 refers). This can generally be achieved by:
(i) locating socket-outlets to provide reasonable sharing of the load around the ring
(ii) not supplying immersion heaters, comprehensive electric space heating or loads of a similar profile from the ring circuit
(iii) connecting cookers, ovens and hobs with a rated power exceeding 2 kW on their own dedicated radial circuit
(iv) taking account of the total floor area being served. (Historically, limit of 100 m² has been adopted.)
Reading that we should really have dedicated supplies for washing machine and tumble dryer, I know we don't, but where in the ring final we take high loads will make a difference.
In the main a washing machine (not washer/drier) takes high current for too short of a time to really worry about, so really looking at the tumble drier, I know our old vented type was 1 or 2 kW there was a switch to select, we always used the 1 kW setting, the new heat pump one not sure on how much power it uses, but unlike the element the heat pump does not run all the time, however as with any refrigeration device we are looking at volt drop, unless inverter controlled.
So start point is the readings, loop impedance at the consumer unit and loop impedance at the point you want to take a radial from will show the volt drop already existing and how close to centre of the ring final you are, the R1 + R2 readings will show how much cable already in the ring final, it is considered 106 meters to be the limit.
But without readings we are guessing, as an electrician I can make an informed guess, based on similar homes, but without seeing the home, I can't even guess how close already sailing to the wind, so can't really answer the question.
Any other method is trusting to the lord, and in the main we get away with it.
In my first house in the early 70's we washed in the kitchen, we dragged the twin tub to centre of the floor, and while washing, no cooking was done, the next house had a kitchen extension so the washing was done from a independent ring final and in the dinning area, so food and cloths did not really mix, and this house we have a utility room, so no cloths washed in the kitchen, and all the cooker was not in any way connected to the ring final in the kitchen, so no great load on it, this house ring split side to side of house, so loading of the two rings more even. Not worked out why rings ever split upper and lower seems an odd way to split.
So we can give pointers, but without readings your guess is as good as mine, likely better as you know the home.