Keeping with the prepositions theme (a rich lode), British and American speakers use different ones when referring to the telephone. To be more precise, on both sides of the Atlantic we talk about calling on the phone, on a mobile, or on a particular day of the week; and we all say, “Call me at noon.” However, they say, “Call me on 555-555-5555,” while we say, “Call me at” a specific number. Or, we did do; the British on is creeping in.
I don’t have many published references, since this is very much a conversational deal. However, Stephen Hunter’s 2009 novel “Night of Thunder” contains this voice-mail message by a character: “Nick, Swagger. I have to run something by you and sooner would be so much better than later. Call me on this number please, bud.” And the internet is full of instructions such as this one, from performance-anxiety.org: “Call me on 1-888-512-2913 or use the contact form here to request a callback …”
Finally, the rapper known as C-Murder (who is currently serving life imprisonment following his conviction for a second degree murder committed in 2002) has the following lyric in his song “Betya”:
You can call me on 1-900-break bread
Or 1-800-getting paid but don’t tell
Or imma send Cut Boy to rang yo bell
notoneoffbritishisms.com 
Another Britishism that this post brings to mind: the British use mobile (versus “cell” in the US). I’m not sure whether mobile is gaining ground in the US or not.
https://britishisms.wordpress.com/2011/03/28/mobile/
I used to correct my (Scottish) boss’s press releases when they said “call us on 93XXXXXXX”… and then I just gave up. And now I use it. I also say mobile and call the letter Z “zed.” Oh well!
From the early ’80s to the early ’90s I sold stuff to a large phone company on the east coast of the States. When my customers gave me their phone numbers, they uniformly said “Call me on ….” I fgiured that was a phone company convention.
I would argue that in the UK we use the term “ring me” more than “call me”, or even more common “give me a ring.”
Well, “Call” as opposed to “Ring” is an Americanism isn’t it. When I was a lad, “give me a ring” was the lingo. People didn’t “call” you, then “rang you up”.
Today though, in my London office, “Ring me” would seem archaic. Everyone “calls” now.
‘Call’ is definitely an Americanism. ‘Phone’ is another more traditionally British variation. A radio show may have a ‘phone-in’ where listeners get in touch. That said, ‘call’ has become more and more common in recent years.
Indeed, BBC Radio 5 live’s breakfast phone-in is now named “Your Call”.
I remember a sentence from an early Robert B. Parker book (Promised Land, 1977):
‘What’s the wording for your ad?’ I said.
‘If we get separated? We just say, “Sisters, call me at”– then we give a phone number and sign our first name.’