It's a fairly simple operation but I struggled to find much on the internet to assist prior to starting so have written this to help others.
New batteries are available from ebay, search for "Tom Tom One V3 Battery" and you should find loads. Expect to pay about £8-£10 delivered.
You will also need a Torx 8 or T8 driver to remove the screws. These are available in the UK from Maplins, B&Q and Screwfix, often in a combined security driver pack.
Before you start:
Remove any SD cards
Backup the TomTom using the TomTom suite software supplied with the unit. You shouldn't affect any data on the unit but best be safe!
Step 1: Remove screws and open case
Once removed use your finger nails or an old credit card to open the case at the top, it splits between the silver and grey section as shown. Once as shown the grey back section slider down off the unit to clear the SD card and USB port.
Step 2: Lay out and remove old battery.
If you feel any resistance the wires are still retained in the cable clip and just need freeing up.
Now you need to free the battery. It is held down with a sticky foam pad. I found that inserting a slotted screwdriver in the now empty hole for the USB connector allowed me to work it loose. Be careful as if you go silly you could puncture the battery (unlikely though).
Once the battery is loose you need to disconnect the lead. This is a small three pin plug and needs to be gently pulled upwards away from the circuit board. You may need to work a small screwdriver in to release if very stiff.
Step 3: Install new battery and close up.
Make sure you install the battery with the power lead to the top left as per the original. My battery is flipped here to show the sticky.
Insert the new battery and attach the plug to the socket on the circuit board. The plug is 3 pin and must be connected the correct way. If you look at the plug you can see the pins are offset so in theory will only connect the correct way. However I'm sure with enough force you could mash it in the wrong way so take your time.
Once done bring the two halves together like a book, and route the two wires in the cable clip. Then assembly is reverse of removal, slide the grey halve onto the silver half so the USB connector pokes out of the hole in the case. If it looks correct snap shut and screw back together.
Step 4: Turn on, check and charge up.
Although the battery was in theory supplied charged when I went to the Status Summary sheet as per below it began to charge. I left it charging like this for at least 6 hours to ensure it was fully charged and to avoid battery memory.
All your existing data on the Tom Tom should be as before, if by some freak chance you have lost any data they reinstall from the backup made at the start.