UKH

A cheap second hand one, Wigan to London.  Any tips?

Wheels, seat and pedals off. Bars off and taped to the frame, so all cables can remain connected. 

Then measure up and use one of the comparison sites. Chop up a few plastic bottles to use as end caps on the forks etc. That could get damaged or burst through the packaging. 

Use and old axle or improvise a spacer between the forks and the stays to prevent them from being crushed

If its a cheap second hand bike, probably cheaper to sell it and buy another one in London.

Otherwise there are a few couriers that will take bikes (and motor bikes) - not sure how this would compare to a postal service

An answer a bit left of centre, but if you are flying, some airlines let you take a bagged bike free. I sent a bike from southern Italy to my door in Melbourne for 300 euros, by courier, but I could have had it as my luggage for free on Etihad.

Sadly a cheap  bike doesn’t cost less than an expensive, to post 

Could you not get a friendly scrapyard to compact it into a neat cube, then pop it on My Hermes for a fiver?

Grossly overpriced at that. Your parcel could end up anywhere. 

Not wrong there!
I've just  bought two bikes off fleabay recently for £90.  One a mid range mountain job and a 'Ladies' one for my very occasional bike riding daughter.  Both virtually brand new.  Ridiculously cheap!

Go to Halfords and get a cardboard bike box for free. They have loads and give them away.

Box the bike up then use an online bicycle postage courier. They collect it and deliver it for about £25

Many of the couriers just act as agents for TNT, who once drove a sharp object through the carton and damaged a bike I sold on Ebay. The buyer's muppet wife then signed for it "in good condition" despite there being a big hole through the box, meaning we had a hell of a battle getting recompense from TNT. So whatever you do, tell your buyer to check the package  carefully for signs of damage and if not happy sign for it as "damaged". 

Paisley Freight have a good website for sending all kinds of stuff. 

Got a spare Sunday?  Take a London Northwestern train to London (slow and unreliable but dead cheap) and go and get/deliver it yourself, you get a day out in the price too.

If the wheels are quick release, I use a couple of washers, a bit of old copper pipe and the skewers.

You can re-thread the pedals the other way through the cranks, so they can't get lost or fall out of the box, otherwise wrap in bubble wrap and tape to the frame.

Rear mech hangar is pretty vulnerable in transit. If leaving the rear wheel on, shift rear mech to the largest sprocket and pad with cardboard over the top. If taking the wheels off, unbolt the mech and tape it between the chainstays.

You don't say if the bike has disk brakes, but I've found they're pretty awkward to pack around without damage and resorted to removing them, bagging them and taping them to the spokes.

I've used paisley freight before and they did a good job.  Old cardboard bike box free from halfords or local bike shop, if you're lucky it will come with plastic axle spacers and a bit of wrapping as well.