The blasted (literally) lightning strike last night seems to have fried our answerphone, and it doesn't look as though they are available in the UK any more - does anyone know differently? As you can imagine, an answerphone is a necessity when you have ME, and we really need a standalone one. Apart from the fact that there's nowhere appropriate to set up a base station, so a cordless is out of the question, we have enough phones already and don't need to be buying another one just because it's a combined phone/answerphone. Also, the quality of combined phone/answerphones is usually lower than for a standalone.
Sometimes it works out best to just go with what's currently the most mass market product, even if it's not really what you want. I'd expect that a answering machine/phone would be cheaper than a rare solo answerphone. I might have misunderstood you, but you could have a cordless phone in one position, but still use your other wired phones too.
You could look into buying a working 2nd-hand one on eBay - I did a quick search and found quite a few: https://www.ebay.co.uk/sch/i.html?_from=R40&_nkw=(answer,+answering)+machine&_sacat=139968&LH_TitleDesc=0&rt=nc&LH_PrefLoc=1 . We still stick with our old answerphone, even though BT recently renewed our account by cutting off our copper wiring connection and switching it over to broadband-based (without our knowledge or consent, bah), but thankfully our old gear still works. I do agree that the quality of new gear (at least, the combined cordless phone/voice mail answerphone they provided with the renewal) is poor quality, so am glad we can still use our old phone & answerphone with the new system.
I have an old model of this : https://shop.bt.com/products/bt-7660-twin-109337-GMC0.html You can leave it where it is or carry the handset around. It can be bought as a single handset, or with 2, 3 or 4 handsets. You can listen to any answer machine messages from any handset. Another useful feature of these phones is that one handset can call another in the house. So if you are trapped in your bedroom you can call someone in the living room, for example. Or what about the BT 1571 service? According to this fairly recent link, it is a free service : https://community.bt.com/t5/Home-phone-including-Digital/Landline-Voicemail-1571/m-p/2237875#M84787 More info : https://www.bt.com/help/landline/using-bt-answer-1571-voicemail
There is this one - very traditional, and includes an answering machine : https://shop.bt.com/products/bt-decor-2600-premium-nuisance-call-blocker-083154-BTHZ.html
Ah. I think that may be a major problem. Are you saying that you can't hear the message while it's being recorded? That's absolutely no use. The person concerned needs to be able to hear the message in order to intercept it and pick up the phone. I fear EBay/Amazon is going to have to be the way to go ...
And yes, it's quite well-known that the quality/reliability of the phones_with_answerphone is much poorer than that of standard answerphones.
This is the user manual for the phone with 1 - 4 handsets : https://shop.bt.com/content/uni2/documentation/gmc1/bt_7660_user_guide.pdf Page 44 describes the Call Screening options which is what you are describing (I think).
I had one too, and they were great. You could choose whether to screen calls or not. I remember it looked complicated to set up because there were a lot of functions, but once I'd found my way round it, it was easy to use.
I have a Panosonic and if someone leaves a message you can hear it on all of the handsets as it's being recorded.