Since Brexit, I have rarely used my Amazon UK account, as the customs tax on items can be prohibitive, along with ridiculous delivery duration, sometimes exceeding a month. Amazon de is a different story. I order from them, but much less over the last six months, as prices have risen significantly and delivery costs on some items, exceed the cost of the item!. However, I will say that the delivery times have improved, as they now use FAN Courier, a Romanian company - on average you wait 7 days for delivery. If you're not in, when FAN Courier tries to deliver, they will deliver the item, automatically, to an Econt office, to which you will be charged a service fee of around 4 Leva.
You should also note that certain Amazon items, such as batteries, cannot be delivered to Bulgaria.
I'm lucky living in Varna, with so many shops and business selling everything, so I now buy locally.
As for the post, Bulgarian post is never going to be the fastest and add that to Royal Mail strike action in the UK and you're looking at around one month delivery times both ways! I recently received a book that I ordered from the UK - it arrived at the end of January, after ordering it in August last year! If you're posting anything, you'll need to go to a post office. It's pretty bureaucratic and reminiscent of the Soviet days. I once tried posting a letter in the post office in Veliko Tarnovo - it took 30 minutes to achieve a result and you need your ID. Collecting from a post office, is a little simpler, you need ID and it's a good idea for them to have your mobile number, so they can notify you of a delivery. Generally, the post office will not deliver parcels to your door, you have to collect them from your locally designated (by them) post office.
Depending on where you are, if you want a reliable fast delivery service, I recommend A1 Couriers , who also use DHL - it's quite expensive but reliable. I sent medication with A1 Couriers to my Aunt in the West of England and she received them within 4 days.
On another note Speedy (Part of the DPD Group) cannot send anything to the UK! Incredible, considering DPD are in the UK!
Econt have a DHL service but it is significantly more expensive, compared to A1 Couriers.
That said, both Speedy and Econt are usually excellent at deliveries within Bulgaria and the Balkans. You will also find, if you order items from Bulgarian websites / companies, they have a system of pay on delivery at either Econt or Speedy. This is excellent, as you can check the goods before paying and if they're not exceptable, return them no charge. I'm lucky, I have a speedy and Econt office within 75 metres of my door and they're both so useful.
The other option, is to find an expat returning to the UK / coming from the UK and ask them to post locally either end.
Hope this helps.