If you are in the UK and your current UK leave to enter/visa is due to expire on or before 31 May 2020, you can apply for a Spouse/Partner visa from within the UK. (Please note that UKVI will come up with a new guidance usually in the last week of May for individuals whose visas are expiring after 31 May, depending on the latest Coronavirus situation at the time)

However, please note that the Applicant will have to meet all the requirements for the Spouse/Partner visa. Tuberculosis (TB) test requirement is compulsory as per the Appendix FM for applicants resident in certain countries (see list here: https://www.gov.uk/tb-test-visa) . Hence, the only work around would be to file for a visa extension application, see details here: Coronavirus (COVID-19) - UK visas - Latest guidance published on 24 March 2020, updated:6 April 2020)

Then once your visa is extended beyond the 6 months, you can continue to live in the UK and you can file the Spouse/Partner visa application on any day when you complete 6 months plus 1 day or more living in the UK, and then you will be exempt from meeting the TB test requirement as you would have lived for at least 6 months in a country(UK) where TB screening is not required by the UK.