Is this a fault with the phone or line?

[#1]

If someone leaves a message on 1571, I cannot dial out as the beep beep beep does not cancel out.  I take out the batteries and put them back press search (hunt) and I can then call out.  This happened to one of the phones that was not working properly and now affects the other, hence I think it may be a fault with PN 1571.
This is on a DECT phone about 6 yrs old.

[#2]

I don't understand your analysis. It appears that you had a two handset system and one handset developed a fault that exhibited the symptoms you have now, yet you think the second handset has not developed the same fault?
Have you tried using just a corded phone or even a different DECT handset with the old one turned off/batteries removed? Does turning the handset off without removing the batteries cure the problem (often press and hold the "end call" button, same to turn on again)?
Phil

[#3]

Beep beep beep doesn't sound to me like the alternating 1571 message awaiting tone.  It does remind me of experiencing something similar yesterday, when I heard beeps when trying to alter my answerphone greeting from my DECT phone, but not getting any respoinse.  It was in fact a warning that another device, either another DECT phone or the base unit, was in active use at the time.

[#4]

Beep Beep was my bad, phone did make the message awaiting tone. 
Only have the one handset - other is in the recycling, will sort another DECT out come payday.