At least for
Tier 1 (General) workers, as per the
Immigration Rules Part 6A ¶245E, you
do need to be employed or self-employed at the time you apply for ILR:
To qualify for indefinite leave to remain, a Tier 1 (General) Migrant must meet the requirements listed below. If the applicant meets these requirements, indefinite leave to remain will be granted. If the applicant does not meet these requirements, the application will be refused, unless the applicant qualifies for leave to remain by virtue of paragraphs 33E to 33F of these Rules.
Requirements:
(a) The applicant must not fall for refusal under the general grounds for refusal, and must not be an illegal entrant.
(b) The applicant must have spent a continuous period of 5 years Lawfully in the UK, of which the most recent period must have been spent with leave as a Tier 1 (General) Migrant, and the rest may be made up of leave:
 (i) as a Tier 1 (General) Migrant,
 (ii) as a Highly Skilled Migrant,
 (iii) as a Work Permit Holder,
 (iv) as an Innovator,
 (v) as a Self-Employed Lawyer,
 (vi) as a Writer, Composer or Artist.
(c) The applicant must be economically active in the UK, in employment or self-employment or both.
(d) The applicant must have sufficient knowledge of the English language and sufficient knowledge about life in the United Kingdom, with reference to paragraphs 33B to 33F of these Rules, unless the applicant is under the age of 18 or aged 65 or over at the time the application is made.
A plain reading suggests that you must indeed not be unemployed when you apply for ILR. (
¶33E-33F reference rules for extension of stay once ILR is applied for.)
Similar rules apply for
HSMP ILR applicants:
Requirements for indefinite leave to remain as a highly skilled migrant
135G. The requirements for indefinite leave to remain for a person who has been granted leave as a highly skilled migrant are that the applicant:
(i) has spent a continuous period of 5 years lawfully in the United Kingdom, of which the most recent period must have been spent with leave as a highly skilled migrant (in accordance with paragraphs 135A to 135F of these Rules), and the remainder must be made up of leave as a highly skilled migrant, leave as a work permit holder (under paragraphs 128 to 133 of these Rules), or leave as an Innovator (under paragraphs 210A to 210F of these Rules); and
(ii) throughout the five years spent in the United Kingdom has been able to maintain and accommodate himself and any dependants adequately without recourse to public funds; and
(iii) is lawfully economically active in the United Kingdom in employment, self-employment or a combination of both; and
(iv) has sufficient knowledge of the English language and sufficient knowledge about life in the United Kingdom, unless he is under the age of 18 or aged 65 or over at the time he makes his application.
Indefinite leave to remain as a highly skilled migrant
135GA. Indefinite leave to remain may be granted provided that the Secretary of State is satisfied that each of the requirements of paragraph 135G is met and that the application does not fall for refusal under paragraph 135HA.
Refusal of indefinite leave to remain as a highly skilled migrant
135H. Indefinite leave to remain in the United Kingdom is to be refused if the Secretary of State is not satisfied that each of the requirements of paragraph 135G is met or if the application falls for refusal under paragraph 135HA.
Additional grounds for refusal for highly skilled migrants
135HA. An application under paragraphs 135A-135C or 135G-135H of these Rules is to be refused, even if the applicant meets all the requirements of those paragraphs, if the Immigration Officer or Secretary of State has cause to doubt the genuineness of any document submitted by the applicant and, having taken reasonable steps to verify the document, has been unable to verify that it is genuine.
