This is where the backwardness of the UK (BT) telephone system may work to your advantage. If the people you are ringing have Caller ID (whereby the incoming number is displayed on their telephone) then that will show up a UK number calling them in full. Similarly if they dial 1471 after the call has ended and before anyone else calls them then a machine will give them the previous caller's number. In both cases this assumes the caller did not block the disclosure when making the call. However, if the incoming call originates abroad then the information, although transmitted by the overseas telephone exchange, does not reach the UK receiving telephone because BT do not process it. In the case of caller ID the display will say "Unobtainable" and in the case of 1471 the machine will state that "We do not have the caller's number" as far as the receiver of the call is concerned, this can be for any reason including the call originating abroad.
This has been the case with BT lines/exchanges (and any provider leasing BT lines, such as TalkTalk) until very recently. I cannot say for non-BT lines (cable, etc.).