China Doll is correct.
A verbal warning, despite its name, is given verbally, then you should get a letter confirming that you were given a verbal warning regarding your xyz (whatever the issue was). That letter is the thing that you get and sits on your file.
If things aren't working out, I'd take the money and run - depending on your prospects and job situation - only you can judge that.
You need to get them to explain to you exactly how they are proposing to deal with the termination of your employment. They are duty bound to pay you for your notice period but I doubt that is 3 months - typically it would be one month, or one week per completed year of continuous employment if you have worked there longer than 5 years (i.e. 5 weeks after 5 yrs etc.), which is the statutory rules that overrides whatever is in your employment contract - if it is longer.
The REST of the notice period could be being handled in one of two ways:
The leave you on the payroll (which is what you suspect) and you continue to be paid, you pay NI and tax, and you accrue holiday and pension entitlements. You last day, is the final point where they stop paying you.
OR, they make you a payment as compensation for loss of office for the rest of the money. THIS money does not incur tax or NI - so it makes a difference. You last day, from a legal point of view (and what appears on your P45), would be the date the notice period runs out.
In exchange for agreeing to one of the above, they will very likely ask you to sign an agreement that you will not work for a period of time (the Gardening Leave period).
As a person formally involved in personnl management and recruitment, I'd say that recruitment people accept that sometimes things don't work out and one takes interviewees as one finds them at interview. Be prepared to explain your side of the story during interview - any reference from your current employer is more