Yes, David Austin shrub roses will grow from cuttings. In fact, the only one in my garden that has refused to do so is English Elegance. I have tried for years to root some cuttings of English Elegance because it's one of my favorite Austins, but the cuttings wither away and die without growing roots.
The only other rose in my garden that stubbornly refuses to produce viable cuttings is First Kiss, a floribunda.
These two roses have always been conspicuously absent from the own-root roses offered by most nurseries, so it's not just a matter of my technique.
Frank you said: "Own-root roses!! Not easy at all, if even possible with "modern HT's"! My answer to that is yes and no. It's not easy, but it certainly is possible.
I personally am heavily biased against own-root hybrid teas, but as in all cases, it depends on the rose and it depends on the nursery. Most of my hybrid teas are grafted, but many hybrid teas are no longer available in grafted form, so I've bought hundreds of own-root hybrid teas over the years, with mixed results.
The thousands of dollars I spent on own-root hybrid teas from Vintage Gardens and Heirloom might as well have been thrown in the garbage. All but a few failed to grow well on their own roots. Some of the same roses from VG and Heirloom that failed actually did grow well when I bought them from other own-root nurseries, however, so some nursery practices clearly work better than others. Unfortunately, most of the nurseries that supplied me with viable and vigorous own-root hybrid teas have gone out of business -- Amity, Ashwood, The Uncommon Rose, Sequoia, Moore's, Roseland, and a few others. If I wanted to buy more own-root hybrid teas today, I'd look for them at Northland Rosarium and Roses Unlimited.
