Juni, maybe try posting in SN children as well, much busier board than SN Education.
I'm not in London, but my DS2 with statement is managing well in a MS secondary. It's big enough to have a lot of MLD and or autistic DC, which gives it much more experience than a primary. They teach a small group of DC in each year group outside of the MS sets in the 'learning skills' department. They are taught English and maths there during timetabled English, maths and MFL lessons. So they miss learning a MFL but use that time to boost their English and maths.
It's not a 'special unit' as such, but has many of the benefits of one. The DC are back with the MS classes (some set by ability, some mixed ability) for humanities, games, art, music, DT etc so benefit from the MS specialist facilities for those subjects.
It would be worth your while contacting the SENCos at your local schools and asking for a visit to see what they offer. You should have a case officer at the LA who can get you a list of all the special schools and special units locally. If not then badger the SN dept at the LA for one.
The advantage of a statement (not sure about EHCP, DS not converted yet) is that the admission process is separate from everyone else giving you potentially more choice to find a school that is suitable.
Good luck.