If you do have a look in a charity shop, vehicles and action figures tend to be popular with that age, simple books, simple puzzles, first board games like bingo/lotto types - if you can find any of the Orchard Toys brand they tend to be very good. But there's lots you can do for free.
Set up a pretend shop. You can use real coins and 'sell' actual food, or any sort of household bits.
Maybe they could draw a picture for mummy and daddy. They usually like it if you sit alongside them drawing too.
Cutting and sticking, if you have any old magazines or catalogues with colourful pictures.
A long bath with lots of bubbles and a few different plastic cups, bottles, spoons etc.
They're usually happy to help with some basic household tasks. Give them a damp cloth and direct them to some surfaces that need a wipe down; get them to match the pairs of clean socks; have them help you cook dinner.
Search for the following on Youtube, which are all follow along:
GoNoodle - they do really fun, silly songs and dances.
My kids also loved Apples and Bananas by Super Simple Songs.
Or for something calmer, but still made very fun for kids, CosmicKidsYoga.
If you have a library card you can set up a free online audiobook account with Libby or Borrowbox. That way when you need some downtime they can listen to a story.
In terms of going out in bad weather:
Swimming, soft play, trampoline park (at ours there is a discounted rate for younger children in the mornings, and you also find there are fewer boisterous big kids around if you go early).
Our local covered shopping centre currently has a Lego animal trail, which was a free activity my DD loved, and my DH was able to combine with a little bit of shopping. Do you have anything like that nearby?
We also have a small, free, local museum that often runs craft activities at weekends and holidays.
Libraries usually put free kids activities on as well.
Have fun!