Explain the process and timeframe through which your proposal might then become law.

The process for changing a law in the UK involves several stages and can take a considerable amount of time. Here's a step-by-step explanation:

1. Proposal Stage: The first step is to draft a proposal for the change in the law. This could be done by a Member of Parliament (MP), a government minister, or a group that has the support of an MP or minister. The proposal needs to clearly outline the changes and the reasons for them.

2. Bill Stage: The proposal is then turned into a bill. The bill is a draft version of the law that includes all the proposed changes. It is usually drafted by legal experts.

3. Introduction to Parliament: The bill is then introduced to Parliament. It can be introduced in either the House of Commons or the House of Lords. The MP or Lord who introduces the bill is known as its sponsor.

4. Parliamentary Debate and Scrutiny: The bill goes through several readings and stages in both Houses of Parliament. This includes a general debate on the principles of the bill (second reading), a detailed examination of each clause of the bill (committee stage), and a final chance to amend the bill (report stage and third reading).

5. Approval by Both Houses: The bill needs to be approved by both the House of Commons and the House of Lords. If either House proposes amendments, the bill may go back and forth between the two Houses until they both agree on the final text.

6. Royal Assent: Once the bill has been approved by both Houses, it receives Royal Assent from the monarch and becomes law.

The timeframe for this process can vary widely, depending on the complexity of the bill, the level of controversy or opposition it faces, and the legislative timetable. It can take anywhere from a few months to several years for a bill to become law.

In terms of the specific proposals to change the Equality Act 2010 and the Health and Safety at Work Regulations 1999, the process would be the same, but the timeframe could be different. Changes to primary legislation (like the Equality Act) typically take longer than changes to secondary legislation (like the Health and Safety Regulations), because they require a full Act of Parliament rather than just a statutory instrument.