ACROSS: 1. Spur, 5. Coy, 8. Spa, 11. Hare, 12. Abe, 13. Hug, 14. Ali G, 15. Restore, 17. Renoirs, 19. Horn, 20. Poe, 21. See, 22. Reed, 23. Fly, 24. Jedda, 25. Gable, 28. Sue, 29. Aria, 30. Sud, 31. Abs, 34. Fang, 35. Trodden, 37. Frasier, 39. Eire, 40. Ear, 41. Mae, 42. Bega, 43. Sty, 44. Ply, 45. Tusk.
DOWN: 1. Sharp, 2. Paleo, 3. Urine, 4. Rego, 5. Carrey, 6. Obese, 7. Yes, 8. Shooed, 9. Purred, 10. Agenda, 16. Three, 18. Isle, 23. Flags, 24. Judo, 25. Gaffes, 26. Ararat, 27. Binary, 28. Surrey, 30. Steal, 31. Adieu, 32. Bergs, 33. Sneak, 36. Debt, 38. Imp.
The May crossword was set by LR: twitter.com/LRxword