I take my towbar off when not in use but as its seized, I have to remove the nut & bolt and take the whole thing off out of the square hole.
When I refitted it yesterday, I noticed that there is movement up and down even though the nut & bolt are tightened to the max. I can't remember whether it was like this the last time it was on. There is no sideways movement. When I tow, I can hear it clunking.

Has anyone else got play in theirs? 2010 MY Vogue SE TDV8 3.6 Stornoway Grey- fully loaded

No play on mine. I had same issue with seized detachable part. Not sure if you have fixed that but i used a small file on the inside of the receiver and then gave the bearing on the towbar a good lube and worked like a dream L405 4.4 SDV8 Santorini/Black VSE
L332 4.4 tdv8 stornoway/Ivory VSE gone
L332 3.6 tdv8 black/sand vogue gone
Mk 7 vw golf r black/black(swmbo)
Mini Cooper s grey gone (swmbo)
BMW e60 m5 black/black gone
BMW e46 m3 silver/black gone
BMW e39 525i m sport blue/sand gone
Vw mk 4 golf gti blue/black gone

Are there not two holes to put 2 bolts through?? This would create the up and down movement to a certain extent.

It wouldnt matter how tight the nut and bolt are anyway as the metal IIRC is pretty dam thick so wont have any clamping affect  FFRR MY06 facelift With TDV8 Alloys Zeros/ATR's
Mantec Sump Guard, Rigid Load liner, MY10 BT upgrade.

Slight play in mine.
I hope you coated both parts with grease before assembly to stop them seizing in future.

Cut up an old credit card and wedge the right amount of pieces in the square receiver to stop the up and down movement that makes the clunk . 2008 MY Supercharged
Rimini Red / Jet
four zone climate
remote park heater
and no ugly kid windows.
magnus satis quod turpis satis

As axle says, although I used a small piece of ali plate

Andy. 2015 L405 SDV8 Autobiography, Indus Silver with Black Pack.
SWMBO: 22MY Defender 110 HSE X Dynamic, Gondwana Stone.
Gone: 2014 Discovery 4 HSE Luxury Firenze Red
Gone: 2006MY Java Black TD6 Autobiography
Gone: 2013 Jaguar XKR Convertible, Italian Racing Red with Ivory Seats
Gone: 2010MY Stornoway Grey TDV8 Vogue SE with RSE
Gone: 2008 Disco 3 HSE, Hybrid Tv + Retro-fit RSE System & DVD
Gone: 2003 Epsom Green 4.4i Vogue, LPG, Mk4 Nav, BMW Bluetooth Phone, Hybrid Tv Tuner,

I did think about some shims actually. I'll get my mate to craft some for me. 2010 MY Vogue SE TDV8 3.6 Stornoway Grey- fully loaded