I am from the UK as I understand culture might influence the answers.
I have seen some questions similar asked here but I think there are some nuances that should permit this question being asked.
I was asked to interview for job X, and despite not actively looking for work I decided "why not?" as the role sounded interesting to me, so went to interview for job X. Ultimately I didn't get job X but the company did decide they wanted me for job Y. Job Y is basically what I am currently doing so I have less incentive to move to job Y from a career progression standpoint. I am comfortable at my current job and perform very well according to my reviews.
Ordinarily I would just say thank you but no thank you and move on with my life...however job Y is offering me approximately 40% pay rise. At a time when the cost of living in my country is proving very challenging I feel this kind of pay rise is very difficult to say no to. It will have a significant impact on my ability to afford housing, save, and improve the quality of my life. It isn't just me being greedy and desperate for more money. There are significant and tangible benefits from improving my salary now.
It is worth noting that my current company has been promising a review of my salary to make sure I'm being paid adequately and up to what the market is offering for my skillset. I am unaware the current status of this but highly doubt any pay rise will come close to what job Y is offering me.
I am happy my current role, I get on very well with everyone, I am a top performer in my team, and I don't have a desire to leave. I get on with my manager and she understands the personal aspects of work also (as far as my experiences with her have told me).
Is there a professional way (or at least one that won't get me in trouble) to basically summarise the above, something like. I don't want to burn bridges with my current employer.
I have been offered another job doing the same work for a substantial salary increase. With the cost of living increases this will have an improvement on my quality of life. I like working for this company and don't want to leave. Can you match what my offer?