Unless I share this with you, I'll never know if it helps either way...back in 2010 I sold a house. The buyer was using a significant amount of "cash" (money in her bank) to pay for it. Her mortgage was small.
Her solicitor wanted to trace it back further than ten years, but my buyer took massive exception to this, as her money had been given to her by her mother, who lived in another part of the world, and my buyer was of the opinion that it was very personal & all to do with her nationality. Also, as I was told by the estate agent, it can be very hard to trace money in some countries, due to their processes (whatever they may or may not be)
Anyway, such was her unhappiness, she decided the change solicitors, which didn't delay things half as much as we feared, and however she did it, no further questions were asked about her money. Again based on what we were told by the estate agent, it came down to solicitor discretion, so you may wish to phone around other solicitors ask ask if they can take you on, if you are finding this one difficult.
Several years later, a friend of mine bought a house "cash", having sold hers some time earlier & rented for about 18 months. Although there was no issue with anything, I recall it took a lot longer to go through than I ever thought it would for a sale with no mortgage or surveys etc. HTH.