Is it a beep or a chime? If it is more like a chime you could go to Control Panel | Hardware and Sound | Sound | click on Sound tab | click on each Program Events sound and test to see which sound your beeps sound like, then you would know if the sound is a result of one of the Program Events and at least narrow down what may be the cause.

Thanks Vic, I did as you suggested, no one event sounded the same, the nearest was under Windows Speech Recognition the event "Misrecognition" followed by the following event of "Off". Makes no sense that both my computers that are not connected both started doing this the same day and they do it when they are turned On and when they are turned off.   

Maybe a UPS device alarm?

I do not recognize those sounds. You say the computers make those sounds if turned off. What if the power cord is disconnected? Are you sure the sound is coming from inside the computer?

Why would a UPS alarm sound when the computers are turned off though?

If you are getting brownouts or surges it can trip an UPS for a few seconds.

The other condition is that the UPS battery is dying or bad.

https://www.apc.com/us/en/faqs/FA158827/

Cause:

1.) The Back-UPS product is operating on battery power - This alarm indicates that the UPS has transferred from On Line operation to On Battery operation. The Battery Power Supplied outlets are now battery powered.

2.) The Back-UPS product has entered a low battery condition - This alarm indicates that the UPS has reached a Low Battery condition and will soon shutdown. The UPS can only operate on battery for a limited amount of time. In order to protect the unit's batteries from discharging too much, the UPS will shutdown and turn off its output. To warn you that the unit will soon shutdown, the UPS will sound this alarm 2 minutes before actual shutdown. With optional APC management software, 2 minutes can be changed to give you more of a warning of impending shutdown. If you hear this tone, you should immediately gracefully shutdown your operating system to prevent data loss or corruption.

3.) Capacity Overload - This alarm indicates that the UPS has detected an Overload condition. If this alarm is sounded, try removing non-essential equipment. The alarm will remain until the load is reduced. To determine if your UPS is capable of handling the equipment you want to protect, visit APC's UPS Selector.

4.) Unit failed a self test - Most Back-UPS products perform an internal self-test every 14 days, checking the integrity of the battery. If the battery fails the self-test, the ""Replace Battery"" LED will illuminate. The Replace Battery LED is a WARNING that the battery may be near the end of its life, and replacement is typically recommended within 2-4 weeks.

5.) Disabling UPS audible alarm tones  - When using the PowerChute Personal Edition software, the UPS audible alarm tones can be disabled. (Not available on all Back-UPS Models)

Why would a UPS alarm sound when the computers are turned off though?,and it would be too much of a co-incidence for both PCs to have the same fault at the same time. Is it possible that something about my modem could have done something to both PCs as I use the same one modem between the two though not at the same time. 

Yes, on both computers it comes from the computer itself, not through external speakers or headphones. I turn the power supply off so they must be coming from the internal battery. The only connect between the two computers is that I use the same modem for both, though never at the same time, via LAN cable, not Wi-Fi. Both PCs make the sound when off as well as on, even when not connected to the modem. 

I have turned the computer event sounds off now on this particular PC, from time to time I hear a sort of noise as if something is trying to connect via my telephone line coming through my external speakers.

Step 1: Enter sound in the search box and click Sound in the list to open Sound settings.
Step 2: In the Sound dialog box, open Sounds and choose Off under Windows Speech Recognition in the program events.
Step 3: Tap the bar where Speech Off is and choose a sound from the menu provided.
Or click Browse to select music in your PC. Then, hit OK to change the off sound.

Similarly, to change the on sound, after accessing the Sounds settings,
select On under Windows Speech Recognition in the program events,
click the sound bar, choose a sound (e.g. Ring06) from the list and tap OK.

There are malware programs that try to dial 1 900 numbers via analog modem/fax

https://www.trendmicro.com/vinfo/us/threat-encyclopedia/archive/malware/dial_thaws.b

A dialer (fraudulent version) is a program that uses computer’s modem to establish a dialup connection over the Internet and make the money from calls. A connection is made by dialing a predetermined phone number and connecting to an international or premium rate local phone numbers.

I just rang up my telephone provider who though he cannot access my call record over the last couple of days, has told me I had a block on making any premium rate calls which is a relief.

Whilst I can see one computer getting affected, it seems odd that both got affected the same day?

Would Malwarebytes pick up a dialing infection?

Are you actually using a UPS?

And just turning off the alarm won't solve the problem if the UPS battery is dying, if there's a fault on the mains, etc...