The short answer is no, you cannot apply for British citizenship immediately after getting indefinite leave to remain. There is a mandatory waiting period.
Residence requirement:
Under the British Nationality Act 1981, you must normally have held indefinite leave to remain (or equivalent settled status) for at least 12 months before you can apply for naturalisation as a British citizen. This is part of the broader residence requirement, which typically requires you to have been resident in the UK for at least five years before the date of your application, with the final 12 months of that period being spent with settled status (that is, ILR or equivalent).
If you are married to or in a civil partnership with a British citizen, the residence requirement is slightly shorter. You need three years of residence in the UK, with the final 12 months again being with settled status.
Other key requirements for naturalisation:
1. You must have been physically present in the UK on the date exactly five years (or three years for spouses) before your application is received by the Home Office.
2. You must not have been absent from the UK for more than 450 days during the five-year period (or 270 days during the three-year period).
3. You must not have been absent for more than 90 days in the final 12-month period.
4. You must be of good character.
5. You must have sufficient knowledge of English, Welsh, or Scottish Gaelic (normally evidenced by passing the Life in the UK test and meeting the language requirement).
6. You must intend to continue living in the UK (or to continue in Crown service or service of an international organisation of which the UK is a member, or to be employed by a company or association established in the UK).
Discretion on absences:
The Home Office does have some discretion to overlook excess absences in certain circumstances, but this is not guaranteed and should not be relied upon without good reason.
Practical next steps:
If you have just received ILR, the sensible approach is to note the date it was granted and plan your application for at least 12 months later. In the meantime, make sure you satisfy the other requirements, including taking the Life in the UK test if you have not already done so, and keeping careful records of your travel in and out of the UK. You should also be mindful that the naturalisation application fee is currently substantial (over £1,500 including the citizenship ceremony fee), so it is worth budgeting for this in advance.
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