Who funds the 1:1? Did the nursery have to apply for funding? If so what did they write on the form about what the problems were? Ask to see it.
Does the nursery do a home communication book where they can write what problems they see each day and what they did about them? This can help build evidence as well as let you know what intervention, if any, they are putting in place.
What are they writing in their own records? Ask to see your sons nursery file.
One thing you can do to stop things just drifting along is apply for an Education, Health and Care Plan which is a legal document setting out what help your child needs. If he needs full-time 1:1 he is likely to also need this when he goes to school. You can apply for an assessment to see whether he needs a EHC Plan yourself (see IPSEA which has standard letter although you also need to put in enough evidence to make the council decide assessment is necessary). If he needs FT 1:1 then you will need a Plan in school as most councils only fund 12-20 hours 1:1 without a Plan so you may as well start getting this in place.
One of the reasons you can request the plan is because your child's needs are not known and the assessment is needed to find out the extent of his needs and put in place a proper programme of intervention - because SLT twice a year is not enough. If you don't know what is going on how are the nursery staff supposed to provide a suitable education as presumably they don't know either?
There will be a local parent partnership service that can advise you but they are not always as independent of the council as they should be
As part of the assessment a range of experts Paed, SLT, Educational Psych will see him and have to prepare reports setting out the extent of his needs and the problems he presents with and intervention needed. You may well get turned down initially (Councils try and put off funding as long as they can), but you have a right of appeal and Councils often back down when a parent appeals.
Even if you are turned down its likely the council SEN team will call a multi agency meeting so all the professionals and you get together and talk about your son and put a proper plan together.
You can also self refer to Ed Psych and ask to observe your son and talk to you and explain what is going on.
Pursuing the EHC Plan is the only way to get any legally binding intervention - without that you can just be fobbed off with occasional visits.
You can also apply for DLA - Cerebra do a good guide for children with neurological problems but it can be adapted to any difficulties.
You can also apply to Disabled Childrens Team at social services and ask for them to do an assessment of you as a carer and your child to see if you need any services e.g. respite or short breaks. So for e.g. employ someone to look after one child while you take the other out or an extra pair of hands on trips or just to give you a break.
It is much more difficult when you don't have a diagnosis to get services which is why you have to apply for everything and be prepared to challenge any refusal. If professionals refuse ask them to put that it writing with reasons so you can then appeal if you need to.
IPSEA & Contact a Family are good websites of charities that have lots of info on them about what is available and how to apply.