The Romans placed an emphasis on mining in the Black Country almost 2,000 years before the revolution, and you can read about poor working conditions in both eras. Other than the obvious language barrier, does my life really change that much?
There are a lot of factors at play here. Your mine in 50 CE may be a small undertaking by you and a few friends, individual entrepreneurs. Or it may be a larger affair, with slaves possibly providing or augmenting the labor, and the experiences of the workforce even at that time could vary depending on the circumstance.
For the mines in nineteenth-century Britain, change was afoot, and every decade brought innovations and differences in the approach. Because not every mine integrated change in different ways and at different times, we almost need to ask your time traveler about which mine he is approaching to seeks employment.
At the beginning of the nineteenth century, your Roman-era miner might encounter a locally owned and operated excavation with friends and family providing the labor. By 1850, the mine was more likely run by a larger business concern and the miners were facing increasingly harsh conditions. Their mine would likely have been far deeper than was experienced in the Roman period and the workforce would likely be larger. Depending on the depth and prosperity of the mine, miners would have either descended by ladder or a hoisted rope (much like the Romans) or by a steam-operated hoist - which the Roman miner would have found shocking. The steam engine would likely be pumping water out of the depth - which would also be a curiosity for your Roman-era worker.
In both cases, wooden supports would have been minimized because the wood costs money. Traditional mining in both period tried to rely on natural, native rock for mine supports, leaving "eyes" in the mine (natural pillars of rock left untouched). Safety costs but so does a collapsed mine, so there was always an attempt to balance need and cost, and danger was ubiquitous.
In the Midlands (but not everywhere in Britain), your miner might encounter woman and children working underground. That would probably be a surprise for the Roman-era miner. Women were traditionally regarded as bad luck in a mine, but industrialization was forcing the abandonment of that folk belief.