My most recent purchase came with two key fobs. It was only when I pulled them apart that I realised one of them doesn't have the blade tucked away to open the doors manually.

Is it possible to purchase this part separately anywhere?

Yes, a locksmith or auto locksmith can easily cut a new blade using your existing blade as a template.

Yep, but will they have the blank blade to fit in the 2011 RR key fob?

If the same as in the below video, yes, standard part, nothing special.

One thought, if the blade is missing, is the transponder chip still in the key with no blade? if not you will need a an auto locksmith to set up and programme a new one

Transponder chip is a little black piece of plastic, approx 10mm X 3mm X 2mm dimensions

Yep, the remote still operates the central locking. No idea how they lost the blade.

The transponder is what allows the key to turn in the ignition.
The remote can be programmed to open the doors but without the transponder, the new cut key will not allow you to start the vehicle.
As Merchy has said it's a tiny rectangle of plastic that is the chip.
Us with early BMW fixed blade keys can upgrade to these type of keys, buying the right frequence, off the net but it's the transponder that apparently costs the money. 2005 FFRR SC Java Black with Overfinch Exhaust (UK)
2008 D3 HSE Stornoway Grey (UK)
2008 D3 HSE Izmir Blue (ZA/Zimbabwe)
1995 D1 300 Tdi (Zimbabwe)

I can't quite work out which bit is the transponder but just taking the circuit board out of the damaged fob is enough to unlock and start the car.

On the downside, it appears that the small spring, case release button and the small metal clip are missing from the damaged fob I have.

Also just noticed that the previous owner managed to lose the battery tray also. How the hell do you lose the battery tray and not realise?

The scenario may well be similar to one I had. Lost the key, but the cost of a new one from JLR was so I bought a used one from eBay and used the IID to program it to the car. I threw the blade away and never quite got round to having a new one cut.

The 2010+ cars don't have any option for turning the key in the ignition as they're push-button start.

So you just need the key to open the door if the battery goes flat - my car only came with one key, but it's possible they just supplied one key with a blade after 2010 as it's only needed as a spare, just a hunch.

You can also buy a later style key (as pictured) and program it to the car using an IID Tool or similar, doesn't give you any additional functionality but it's a nicer/smaller key and looks a bit more modern

This shows the transponder. 2005 FFRR SC Java Black with Overfinch Exhaust (UK)
2008 D3 HSE Stornoway Grey (UK)
2008 D3 HSE Izmir Blue (ZA/Zimbabwe)
1995 D1 300 Tdi (Zimbabwe)