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Inclusion criteria:

1. Patients must have a confirmed diagnosis of multiple sclerosis according to revised Mc Donald criteria and have entered the secondary progressive stage or a diagnosis of Primary Progressive MS.(Polman et al., 2011, Lublin, 2014) Steady progression rather than relapse must be the major cause of increasing disability in the preceding 2 years. Progression can be evident from either an increase of at least one point on the EDSS or clinical documentation of increasing disability.
2. EDSS 4.0 - 6.5 (inclusive).
3. Male and Females aged 18 with no upper age limit
4. Females of childbearing potential and males with partners who are of childbearing age must be willing to use an effective method of contraception (Double barrier method of birth control or True abstinence) from the time consent is signed until 6 weeks after treatment discontinuation and inform the trial team if pregnancy occurs.

   For the purpose of clarity, True abstinence is when this is in line with the preferred and usual lifestyle of the subject. Periodic abstinence (e.g., calendar, ovulation, symptothermal, post-ovulation methods), declaration of abstinence, withdrawal, spermicides only or lactational amenorrhoea method for the duration of a trial, are not acceptable methods of contraception.
5. Females of childbearing potential have a negative pregnancy test within 7 days prior to being registered/randomised. Participants are considered not of child bearing potential if they are surgically sterile (i.e. they have undergone a hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or they are postmenopausal.
6. Willing and able to comply with the trial protocol (e.g. can tolerate MRI and fulfils the requirements for MRI, e.g. not fitted with pacemakers or permanent hearing aids) ability to understand and complete questionnaires.
7. Willing and able to provide written informed consent.
8. Willing to ingest gelatine (placebo will contain this). Participants must therefore be informed sensitive to personal beliefs e.g. faith, diet.

Exclusion criteria:

1. Unable to give informed consent.
2. Those that have experienced a relapse or have been treated with steroids (both i.v. and oral) for multiple sclerosis relapse within 3 months of the screening visit.

   These patients may undergo a further screening visit once the 3 month window has expired and may be included if no steroid treatment has been administered in the intervening period. Patients on steroids for another medical condition may enter as long as the steroid prescription is not for multiple sclerosis (relapse/ progression).
3. Patient is already taking or is anticipated to be taking a statin or lomitapide for cholesterol control.
4. Any medications that unfavourably interact with statins as per Spc recommendations e.g.: fibrates, nicotinic acid, cyclosporin, azole anti-fungal preparations, macrolideantibiotics, protease inhibitors, nefazodone, verapamil, amiodarone, large amounts of grapefruit juice or alcohol abuse within 6 months.
5. The use of immunosuppressants (e.g. azathioprine, methotrexate, cyclosporin) or disease modifying treatments (avonex, rebif, betaferon, glatiramer, dimethyl fumerate, fingolimod) within the previous 6 months.
6. The use of mitoxantrone if treated within the last 12 months.
7. Patient has received treatment with alemtuzumab.
8. Use of other experimental disease modifying treatment (including research in an investigational medicinal product) within 6 months of baseline visit.
9. Active Hepatic disease or known severe renal failure (creatinine clearance \<30ml/min).
10. Screening levels of alanine aminotransferase (ALT), aspartate aminotransferase (AST) or creatine kinase (CK) are three times the upper limit of normal patients.
11. If the patient reports any ophthalmic conditions such as glaucoma, ocular trauma or degenerative eye disease. . Cataracts are acceptable as long as they have not been advised to have surgery. No restrictions on post surgical care, unless the patient reports sight restricting capsule opacity. Short title: Simvastatin in Progressive MS Sponsor code: 16/0730 UCL protocol Version 1.7, dated 18/10/2022 Page 40 of 86
12. Patient unable to tolerate or unsuitable to have baseline MRI scan (e.g. metal implants, heart pacemaker) or MRI scan not of adequate quality for analysis (e.g.

    too much movement artefact).
13. Females who are pregnant, planning pregnancy or breastfeeding.
14. Allergies to IMP active substance or to any excipients of IMP and placebo or other conditions that contraindicate use of galactose (eg. Hereditary galactose intolerance, Lactase deficiency, glucose-galactose malabsorption)

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