Yes, you coud go to Halfords, the supermarket chains or the online retailers and buy something for £100 or less, but you'll probably end up with a bike that 'll put your child off cycling for years if you do.
I know because I made that mistake myself by ordering a cheap bike (a Raleigh as it happens) on Amazon. It weighed a ton and the twist grip for gear shifting was so stiff even I struggled with it. My four year old had no chance. When I took it to my local bike shop to fix it they said it served me right for buying a cheap bike. Bit blunt, but fair cop.
My first tip is to start your child off with a 'balance bike'. There are many out there, and they're amazing. Kids love pushing themselves along on them and soon they'll be balancing between pushes. And better still, when your child is ready for his first proper bike you won't need to bother with stabilisers, and before you know it, your budding Cav or Wiggo will be bombing around the park without a care in the world.
There are loads of brands to choose from, and they can be picked up second hand without too much difficulty.
It's very important to buy the right size bike for your child. One that's too big with brake handles that can't be operated properly will be dangerous, and crashes will only put your child off.
What to look for
Much like buying an adult bike, it's weight, components, wheels and build-quality that matter most, with weight being especially important for children.
Many parents/children opt for mountain bikes, but to be honest the extra weight of the suspension forks isn't really justifiable unless your child is going to be getting involved in some serious off-road action.
It's more of a style issue. Children (well boys, mainly) tend to think mountain bikes are cool because they look tank-like.
So what are the main choices available? Well one brand stands out from the rest.
The Cnoc 14 (also available in red!) weighs just 5.68 Kgs and is suitable for children aged 3+. The Cnoc 16 is a slightly bigger version for age 4+ (still under 6Kgs and much cheaper than a Parlee!)
My six-year-old hated cycling because the cheap pile of junk I bought him when he was three put him off completely. It had stabilisers which were so badly designed that he toppled over twice, completely destroying his confidence, until he refused to get back on it.
Eventually I bought him an Islabike Beinn 20 (7.9Kgs) for his sixth birthday. Unfortunately he refused to ride that as well after an initial wobbly attempt to cycle in our local park ended in failure. I actually had to borrow a balance bike which he secretly used at home when no-one was looking to get the balancing thing sorted. After two goes he got the hang of it. The next time we went to the park I ran alongside him with my hand on the back of the saddle; and the time after that he had it cracked. Of course now he really had the cycling bug and wanted to know why he didn't have a road bike like Cav (we'll come to that later!).
To be fair, there are a few alternatives out there that aren't too bad, but before you buy them check out the weight. They might be made by the big bike brands, but that doesn't mean they'll be as light as the Islabike.
Even the very popular £250.00 Specialized Hotrock mountain bike [left] weighs in at 10.35 Kgs, that's the weight of an average adult bike. According to Bike Radar 'A kilo saved from the bike of a six-year-old weighing 30kg is like 2.5kg saved from an adult's'.
The Giant XTC [right] looks ok for £200 but its weight isn't quoted on the Giant website.
Trek, Scott and others have also dipped their toes half-heartedly into the children's market, without any great success.
Or there's always 2012's take on the good old Raleigh Chopper (£245.00) if your child has a good grip on post modernist irony. But they don't make 'em like they used to.
The Ridgeback MX20 is a big seller at around £200 (14 and 16" versions are also available). It has front suspension which means it weighs a fairly hefty 11.2Kgs
So to sum up, a good quality kids starter bike will cost you more than you might hope or expect, but your child will enjoy it much more, and you can resell it rather than junking it when it's been outgrown.
It'll also potentially cost you a lot less to service and repair as it'll be well made and less likely to go wrong (or fall apart). Cheap bikes often turn out to be a false economy.
Tom and I regularly go for quite lengthy rides (over ten miles) and so long as there isn't an uphill finish he's fine. A bit like me really.