Using a personal phone to contact the security services provides a direct link between that person and the security services to anyone who can access phone records. Using a payphone (probably) at the very least increasing the cost of establishing such a link (to identify the individual, you need listen to the call, which is more work and may be obscured by any OPSEC requirements that can be established over the phone, or have access to some other records [phone location records if the person is carrying a mobile phone at the same time, or CCTV footage from the area]).
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Using a personal phone to contact the security services provides a direct link between that person and the security services to anyone who can access phone records. Using a payphone (probably) at the very least increasing the cost of establishing such a link (to identify the individual, you need listen to the call, which is more work and may be obscured by any OPSEC requirements that can be established over the phone, or have access to some other records [phone location records if the person is carrying a mobile phone at the same time, or CCTV footage from the area]).
Actually you just need to stay nearby - the phones are used to rarely that anybody who uses one is probably a spy.