Bike for 6 year old?

[Lassango]

The wheel size will need to be a 20 inch so I am after any suggestions not knowing much about this type of thing. I will be on the lookout second hand to get more value for money. My budget can reach £150 maybe a little bit more.

All help welcome.

Have a look for a Hoy Bonaly 20 or an Islabike if you're looking at second hand. Or maybe consider one of the rental schemes where you can swap bikes as your child grows.
With kids bikes the lighter weight the better as they're easier to handle.
Bikes for Children | Cycle Sprog

I agree with the PP - weight is crucial. When you consider the bike as a percentage of a child's weight it's not surprising how many children struggle with cheap, heavy steel bikes. Although lighter bikes cost a lot of money there really is a difference, and a good bike is likely to hold it's value if you want to sell it on later. Get the lightest you can afford.
I coach at a kids' cycling club and would say that Islabikes and Frog are still the most popular brands, though Islabikes are no longer in production. There's plenty in the second hand market though and you can still buy spares so I wouldn't rule them out. Other good brands include Woom and Squish, both of whom produce nice little bikes. I've been particularly impressed by the Woom range though unfortunately they are pricey. You might not see as many available second hand yet as they are both relative newcomers to the market, but it's worth looking.
But basically you can't go wrong with any of those brands and all should have decent resale value afterwards.

I would completely agree with the PP above: look at lightweight bikes from Islabike, Frog, Squish and Woom. The weight of a bike really makes a difference for small riders. The secondhand market is amazing for these bikes. We are on our 4th Islabike, and other than the first, all were bought second hand. The two second hand bikes were sold for near to, if the not the same as we bought them for, the only cost was a service.

Thanks for the suggestions so far. Islabikes and Frog do appear to have a bit of a cult following so the prices on the Bein 20 and Frog 52 are looking a bit higher or a very old model. Though I will keep looking out for them as sometimes they have sold within budget. The bikes do look really nice though.

I have spent some time building up a list of alternative alloy bikes and there are lots of good options. The child in question is currently doing really well on their 16inch bike which is 8kg so I think if I can keep the 20inch bike under 9kg they will have no problem adjusting.

Hoy is on the list but im afraid the Woom offering is out of budget.

Vitus is another brand worth considering. They're not as well known as some of the other brands but are decent bikes. They'll probably be cheaper second hand than Frog etc but unfortunately probably also harder to find.
Also Decathlon's own brand B'twin is not at all bad. You fairly frequently see their adult bikes listed in the "best budget buy" lists in cycling magazines. I've no experience of their children's bikes but I notice they have a 20 inch bike with an alloy frame that weighs just over 9kg. It's over your budget new but you might find a secondhand one and as they don't have the same kind of following as the main kids brands I'd imagine they don't hold their price as well. Just be careful though as they also sell some heavyweight steel bikes!
Another thought is that Wiggle currently have their own brand Pinnacle Ash 20 inch kids bike reduced from £400 to £200. Again, I haven't seen one in the flesh but it's an aluminium frame and looks reasonably good for that price.