I have the Panasonic KXTCD 515EM.
It came in a pack, base handset + slave handset from John Lewis. I can't remember how much we paid, but I've just bought an additional handset from this place
Home Phones which I found via eBay. They were fine. Next day delivery and no problems.
They do the triple pack (base unit + two slaves) for £180 inc. VAT so they're not cheap, but they are pretty good.
To answer your questions
1/ At least 3 handsets (or ability add more)
We've currently got five hanging off one base station. Three new Panasonic handsets, one old Panasonic handset and the only one of the Philips handsets we have that still works.
2/ Phone book centrally stored so don't have to program numbers into each handset.
This is where it gets a bit confusing. Each phone has something like a 200 name/number memory. You can send this phone book from one phone to another when you need to update a number although it can be a pain as you need to select "receive" on one phone and "send" on another. There's also a separate 20 name/number phone book that is stored on the base station. All phones have access to this without having to transmit it from phone to phone.
3/ Illuminated display
Yep. Nice blue back lit dot matrix display. very clear
4/ Integral answerphone.
Yes although see comments below.
5/ Easy to use logical interface, I have to say that the BT Diverse phones I used to have but wore out were very logical to use.
Interface is very clear. Most features are accessed using a little Joystick that sits very comfortably under the thumb.
6/ Sensible number of characters to phone book entries
Not sure of the exact limit, but I've got phone book entries of at least 12 characters that display properly and don't exceed the screen width
Pros
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Very clear display
Digital answerphone records very clearly.
Answerphone can be accessed from any slave handset of the same type.
If you have caller ID you can record a short message announcing who's calling for each of the 20 numbers stored in the base phonebook (good fun, but my wife was unimpressed when I recorded the message "*** it's your mother calling again") You can also assign different callers to different categories and have a different ring tone for each category.
Socket for connecting a headset. Useful for my wife as she works from home occasionally and has to dial into lengthy conference calls
No problems with reliability so far (although we've only had them about four months)
Cons
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There's no obvious visible indication that you have an answerphone message waiting. Nothing flashes or beeps. The display just says "1 message" and is easy to miss.
The two phone book system is a little quirky. We tend to use the phone book that's stored on each handset and just remember to transmit updated entries to the other phones when necessary. You can transmit an individual entry or the entire phonebook. Unfortunately transmitting the entire phone book results in duplicates if any of the entries already exist on the phone you're sending it to. For this reason once you've got all the phones in sync it's best just to use the option to transmit individual entries.
Hope that helps