I would try sitting him on your knee and sing interactive songs eg row your boat, horsey horsey etc and see if you get a good reaction eg eye contact and a gesture (does not have to be speech) for more. Also just mimic back his babble and see if he replies - you can have a conversation just with babbling, its the to and fro which tends to be missing with autism. You can also do this with rough and tumble / tickles - pause and see if asks for more.
I suspect even if you got a diagnosis that you would find it hard to get much in the way of intervention. I have found it hard to get much for a child under 3 - autism intervention is counted as education and so falls to the local authority not the NHS (except for speech therapy and OT). I would think you would probably end up with some very woolly advice as few people in UK are really geared up to autism treatment in under 3's (or even under 5's!) Local Authority tend to think he's not in school yet - mine actually told me to go away and wait until he was three and entitled to free nursery place. I didn't go away but 8 months later we are still arguing over provision.
As you don't know if it is autism or not, then you could try following the child's lead which is a key part of Floortime a therapy originated by Stanley Greenspan. It isn't scientifically proven but for a young child about whom you had concerns it would not hurt - his book The Special Needs Child is worth reading. If you are in London you might want to contact MIndbuilders they have a Floortime therapist who I know has written a book about helping a young child with autism. I would suggest you get in touch with her for practical strategies. I'm not saying don't push for a diagnosis, just don't expect it to open any magic doors. Most parents of under 3's with autism end up with just a portage worker and some woolly ideas about singing songs and playing on their level. If you were fairly certain it was autism - and to be honest there are many positives on your list which my son does not do at 3 - then you might want to look at therapies with a good evidence bases such as applied behaviour analysis which I know someone on here started a child on at 18 months with good success - but you would have to pay for those privately to start off with and battle with the LA to pay for.
I would almost suggest you talk to Mindbuilders people first as they would be able to give you some play strategies and would probably be experienced in knowing what signs to look for.
My (non ASD) children did not play with their siblings until they were 2 (both were early talkers and very bright and no social concerns with either of them) and did not play interactively with other children until nearer 3. Its more whether the relationship with you is missing that I would be concerned eg if does not care if you left him in a room of strangers, did not notice when you cried etc. Also children can be delayed with play and social skills but not have autism. My nephew had speech and play therapy from 2-2.5 and is just a different child. At 2 he just carried toys around and looked at his parents like he had never seen them before. Now he is the most social child going.
I wouldn't say ignore your instincts but I would say just read up on strategies yourself - nothing you will do to encourage play skills and shared attention will harm a child.
Does he have any sensory issues? Most children with autism will be over or under sensitive to smell, taste, light, noise etc and tend either to be very easy passive babies or very overwrought cry all the time babies.
I saw your other thread. I have not used them myself but the London Childrens Practice do assessments and are part of Eagle House which runs autism schools.