Reading the answers there is some ambiguity as to your current situation. I'll answer assuming the following
- You have not accepted any offer
- If your current employer could match your offer you would stay
- You care about your reputation with your current employer.
Firstly take a little stock of the situation. If the market rate for you is 25% more than you are getting, it is likely that to replace you your current employer would have to offer that. (Unless you are being underutilized, in which case moving may be better for you).
However on the flip side some companies can't pay more, either due to financial or bureaucratic reasons. Be prepared to move if they can't make the offer you want.
Also 25% is quite a chunk of money, but be careful of the work you will be doing, career progression, benefits and hours expected.
Hopefully you have thought of this and you are prepared to leave if you are not successful in your negotiation.
Right, so as others have said you don't need to put request for a counter offer in your letter. It is just a formal notice. However it can be an effective tool if you wish to play hard ball, and take a little risk.
A resignation letter is a deadly serious way to show that you are serous. Write it print it out, put it in your pocket. Tell whoever it able to negotiate your salary that you need to talk to them.
OK so very clearly explain your situation in the meeting. Don't make it personal. Just be clear is that as much as you like the job, you can't turn down an offer like you are getting unless you get X.
Some people do this without having an offer to back it up. I have seen companies where threatening to quit was the only way to get a decent pay rise. Your boss may think you are doing this.
This is where the letter comes in handy, if they are not willing to negotiate you can hand it in there and then. Make clear that this is the case.
In my experience actually having the letter will help you negotiate, even if it just the fact that it alters your frame of mind. Be very careful to make clear that this is just about you getting paid the going rate, not a personal vendetta or blackmail.
The risk is that after you resign your other offer could evaporate. Unlikely but it can happen.
Most of all don't feel bad. Companies will get away with paying as little as they can get away with. If you can get a chunk more money elsewhere they are under paying you.