Preserves, baking and other kitchen based activities - hygiene may require a new kitchen in an outbuilding if you have pets or use your farm kitchen for incubators, warming lambs, muddy boots etc, so don't assume what you use for your family will do even if you get the theoretical based food hygiene certificate that says you know what you're doing, if your premises can't comply, you can't sell. Two different inspections, your knowledge/practice and the premises/equipment. Plus all the legal requirements on food labelling, from ingredients to allergens in your working environment (even if not specific ingredients) eg if you store or use nuts you have to notify on all products not just those with nuts in.
Egg and produce sales - you can sell at farm gate but not to businesses/third party sellers unless you grade and label, which increases your costs beyond the feed/maintenance.
As soon as you are trading however small, you need to register with HMRC as self employed and fill in an annual tax return so keep every receipt and cash purchase/sales. If you earn less than the threshold you won't pay income tax and it could reduce other liabilities if you have a day job or a partner with other income, so not a bad thing just a bureaucratic hoop.
You also need to inform all insurers relating to your property/contents and check your vehicle cover if you will be using it for any related travel. The instant you have someone buying at your doorstep you have slip/trip risk and need third party cover. If you run courses or other services, you need professional indemnity related to that profession. Any domestic cover will be invalidated unless buildings/contents insurers know you have that additional risk of other people coming and going, and some will not provide that cover so you're wasting money paying for it, others will not add to the premium but may raise questions and/or the amount you pay of any claim made, and most professions have relevant policies that already note the likely risks and specifically cover them for you.
VAT is optional registration until you reach a hefty turnover but some, particularly farm businesses, register voluntarily and get rebates on large machinery/vehicle purchases etc. Sounds good except you then have to add VAT to your sales prices and if your competitors/industry norm is non-VAT sales eg equines which are mainly a leisure market, then you may suffer the fact that potential customers would rather not pay the extra 20% you have to charge. Ditto selling on equipment/vehicles.
HMRC, and local Business Gateway or other organisations set up to help the self employed comply and compete, provide free training and advice on all the above. Best register self employed first and sign up for their courses before you make any expensive decisions, particularly if one of your activities might rule out others or make them more expensive and complex to comply over.