Why are rack mounted rear lights rubbish!

Another vote for the Cateye rack mount - I have a couple of Cateye rear lights that fit it.

+1 for the Seesense Ace. Great little light. 

I have 2 philips safelights, one on the rack of my tourer and one on the seatpost of my road bike (when needed). I was so impressed with the first one, I went out and bought a second one. I find the larger format puts out more light and has a better range. LED's are an intense light source and may dazzle at arms length but many don't put out enough light to be see very far off.

PS I learned here that Spaninga took over making the Philips Safelight.

Busch Mueller lights are very good, get a dynamo wheel hub for a great setup

Another vote for the Spaninga Elips. Spanninga bought up the rights to Phillips' Saferide lights when they pulled out of bike lights a few years back. The Elips is a newer version of the Phillips rear light. 

I had a couple of B&M rack lights - one battery, one dyno powered before getting the Phillips rear dyno light. The B&M lights just don't compare.

I use one of those cat eye brackets with an omni 5 rear light. It does the job just fine. The square on the back of the light has started wearing out after like 5 years use, so I’ve cut a loop from an old inner tube to go round it and stop it rattling over rough roads.

Cateye has a rack mount that is compatible with their standard LED lights (the ones with a square 'foot' that slides into the bracket). I'd be more than happy to use it with the LD600 or LD610 for example (both use 2xAAA, are bright and have excellent battery life).

Smart have a bracket too, the LB608, which I bought for my kids to use with their 0.5w Superflash rear lights. It works fine but the build quality of the light itself (and the standard seat post bracket) is significantly inferior to all the Cateye units I've tried, which have all been excellent.

Cateye do a mount

https://www.amazon.co.uk/CatEye-Multi-Mount-Bracket-544-5620-Reflectors/...

Another vote for the B&M Toplight Line Plus. Wordy name for a decent light. 

I have used one of these packed out with some spare plastic spacers from older lights (or you could use an old inner tube).

https://www.rosebikes.co.uk/cateye-sp12-replacement-bracket-for-tl-ld611...

Can also use cable ties depending on the diameter of the light.

The new See.Sense Ace will mount to a rack

Also have a look at the B&M Toplight Line - I've got a dyno version but they do battery ones too. Available in 50mm or 80mm fitting

http://en.bumm.de/produkte/akku-ruecklicht/toplight-line.html

Spaninga is your friend

https://www.amazon.co.uk/Spanninga-BRASA-Pannier-Carrier-Light/dp/B009MV... there's also the Elips which has an oval shape to the light.

I actually used athleteshop last year but they ceased trading earlier this year leaving many people high and dry without their orders