Hi Dry Guy,
Sorry that you've had to join this club...
Firstly, it's quite usual not to have any erectile function at such an early stage after your surgery. If they didn't tell you this, they were remiss.
I had a prostatectomy in June '22 and still have erectile dysfunction, but you might recover more quickly. It's 'pot luck', it seems.
I believe that it's usual practice to wait until after your first out-patient review with your Urologist (usually about 6 weeks after surgery?) before starting to use a pump. Ask them to refer you for an NHS vacuum pump. I had to be referred to the Erectile Dysfunction Clinic by the Urologist first, and it was they who then recommended my G.P. to prescribe the pump. This delayed the provision of the pump by a few months, so, once you've seen the Urologist, I would suggest that you start using your cheap pump while you're waiting for the real one to arrive. There is some suggestion that use of the pump within 3 months of surgery can reduce risk of permanent penis shrinkage. It is recommended that you use the pump daily.
As Andy 62 has said, you should also be asking for Cialis ('Tadalafil') tablets from your G.P. in order to ensure continuous arterial blood to the penis.
If you have a Kindle device, there is a good book called "Saving Your Sex Life- A Guide for Men with Prostate Cancer" by Dr. John Mulhall. ( The print version is extremely expensive, I believe). He goes into a lot of detail about all manner of things, some of which will not be relevant to your situation. It is also written from an American point of view, so private health insurance is assumed. But he covers all the important stuff, such as erectile dysfunction, urinary incontinence, penile length, vacuum pumps, injections (such as Alprostadil) and Cialis. It was written about 8 years ago, so the science may have moved on a bit since then, but I think you might find some good information there.
Best wishes going forward.
Jed See.