Thanks again everyone for your thoughts, info and links. The problem with the "Baltic Birch" that B&Q sell is that it is closer to "construction" grade then it is to what I need for what is a "toy" or "Children's furniture". Also my large B&Q store only stocks 18mm which is too thick. I have already made a couple of cribs from a sign making material called Forex for my granddaughter, 1 for her house and 1 for my house when she comes around. I used the Forex for 2 reasons; 1. I had it in stock 2. Being the type of plastic it is we could easily wipe it down with a disinfectant wipe when her immunity is low.
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Above you can see both cradles on a table; one assembled one waiting to be assembled
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Here is another shot from a different angle.
She absolutely adores here cradles because throughout her treatments in hospital she has carried 3 things as her essential survival pack:
1. Her Doll
2. Her blanket
3. her drinking cup
If she has those 3 items she can tolerate anything they need to do to her. So her being able to "put her dolly to bed safe and sound" makes a lot of sense.

I have looked and using various grades of plywood and applying a variety of different vinyls but the bottom line is that if you make something for a child there must no be splinters!

This is why I am looking for the same grade of plywood that Ikea have used on this sort of thing:

DUKTIG Mini-kitchen - IKEA

I am planning on contacting a number of people/companies that have been mentioned in this thread on Monday to ask if them if they can supply me with the grade of plywood I am after and I would WILLING ask any timber yard or cabinet maker in my area; North Wales/Chester area, for a supplier or off cuts however the timber yards near me don't seem to have what I need and as yet I have not found any cabinet makers near me.

Over Christmas Anya was feeling pretty good for a few days and we were over at her house playing with her and I videoed her playing with my wife. You can see that she just wants to play like any other little girl; here is the link to the video:

Video0027 - YouTube

Thanks again for all the info and support in my search.