There are several modern options to replace aging cassette tape or floppy disc storage on your Acorn BBC (Master) micro.
MicroSD cards are very popular. You can wire up a 5V compatible (important!) MicroSD board from Adafruit (ada-254) or use a generic Arduino MicroSD board.
This repository contains the KiCad schematic, PCB layout as well as the Gerber files for a simple "MicroSD board to Acorn userport" adapter.