Yes you can. There is one where you input some answers to questions and you eat matched with someone and you then message them whoever suits you and they reply. It means you can work it through your day. I haven’t used it but I came across it one day when looking into online counselling. I think it works out cheaper than seeing someone face to face.
A friend of mine recently had 6 counselling sessions by telephone, NHS funded and arranged through her G.P. It seems that in this area that's the system currently in place. Telephone counselling in the first instance and then depending on how that goes, either further telephone meetings or face to face whichever is deemed more appropriate to meet the patient's needs. She also had one ' One to one' session followed by 6 weekly group sessions which she dreaded and initially balked at but actually found them incredibly helpful.
I had Skype CBT counselling. It was private though. I think I would only go for phone counselling to make up a missed session with a counsellor I'd already been seeing. I think it's important to know them (face-to-face) to establish trust.
I had online counselling via an NHS scheme, all typing, but found it was not effective for me. There was no connection to the counsellor and it felt very standardised and rushed, almost like talking to a scripted customer service person. It is worth a go if you can get it but if it does not work out and you need face to face sessions please try to make time, your MH is so important.